RD Sharma Class 9 Solutions: Complete Guide [2026]

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RD Sharma Class 9 Solutions Chapter 15 MCQs are essential resources for students preparing for their 2026 board examinations. These comprehensive solutions, crafted by our subject experts, specifically target Chapter 15 – Areas of Parallelograms and Triangles. Students can access detailed step-by-step solutions for all multiple-choice questions, ensuring thorough preparation for the academic year 2026. You can find complete RD Sharma Class 9 Solutions Chapter 15 MCQs directly below.

• RD Sharma Class 9 Maths Solutions

Chapter 15 MCQs – Complete Solutions

Class 9 ke students ke liye RD Sharma Chapter 15 ke MCQs bohot important hain. Ye chapter “Areas of Parallelograms and Triangles” par based hai aur 2026 board exams mein frequently poocha jaata hai. Hamare experts ne har question ko step-by-step solve kiya hai taaki aapko complete understanding mil sake.

Question 1.
Agar ek circle ke chord ki length 16 cm hai aur wo centre se 15 cm ki distance par hai, toh circle ka radius kya hoga?
(a) 15 cm
(b) 16 cm
(c) 17 cm
(d) 34 cm
Solution:
Circle ke chord AB ki length = 16 cm
Centre se distance OL = 15 cm
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OA ko radius maante hain, toh right triangle OAL mein,
OA² = OL² + AL²
16
= (15)² + (16/2)² = 15² + 8²
= 225 + 64 = 289 = (17)²
∴ OA = 17 cm
Hence circle ka radius = 17 cm (c)

Question 2.
Ek circle ka radius 6 cm hai. Centre se chord tak perpendicular distance kya hogi agar chord ki length 8 cm hai?
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Solution:
Circle ka radius (r) = 6 cm
Perpendicular distance from centre = ?
Chord ki length = 8 cm

AB chord hai, OL distance hai
Right triangle OAL mein
OA² = AL² + OL²

Question 3.
Agar O ek circle ka centre hai radius r ke saath aur AB ek chord hai jo centre se r/2 distance par hai, toh ∠BAO ka value kya hoga?
(a) 60°
(b) 45°
(c) 30°
(d) 15°
Solution:
r circle ka radius hai centre O ke saath
AB chord hai, centre se r/2 distance par

Question 4.
ABCD ek cyclic quadrilateral hai jisme ∠ADB = 30° aur ∠DCA = 80°, toh ∠DAB ka value kya hai?
(a) 70°
(b) 100°
(c) 125°
(d) 150°
Solution:
ABCD cyclic quadrilateral hai jisme ∠DCA = 80° aur ∠ADB = 30°

∵∠ADB = ∠ACB (Same segment ke angles)
∴ ∠ACB = 30°
∴ ∠BCD = 80° + 30° = 110°
∵ ABCD cyclic quadrilateral hai
∴∠BAD + ∠BCD = 180°
⇒ ∠BAD + 110°= 180°
⇒ ∠BAD = 180°- 110° = 70°
ya ∠DAB = 70° (a)

Question 5.
14 cm length ka chord centre se 6 cm distance par hai. Same circle mein dusra chord centre se 2 cm distance par hai. Dusre chord ki length kya hogi?
(a) 12 cm
(b) 14 cm
(c) 16 cm
(d) 18 cm
Solution:
Circle mein AB chord = 14 cm
Centre se distance OL = 6 cm
r radius maante hain, toh OA² = AL² + OL²
⇒ r² = (7)² + (6)² = 49 + 36 = 85

Same circle mein dusre chord CD ki length = ?
Centre se distance = 2 cm
∴ r² = OM² + MD²
⇒ 85 = (2)² + DM²
⇒ 85 = 4 + DM²
⇒ DM² = 85-4 = 81 = (9)²
∴ DM = 9
∴ CD = 2 x DM = 2 x 9 = 18 cm
∴Dusre chord ki length = 18 cm (d)

Question 6.
Ek circle ka chord 10 cm hai. Is circle ka radius kya hona chahiye?
(a) 5 cm
(b) 5 cm se zyada
(c) 5 cm ke barabar ya zyada
(d) 5 cm se kam
Solution:
Circle ke chord ki length = 10 cm
Circle ke radius ki length chord ke half se zyada hoti hai
10/2 = 5 cm se zyada (b)

Question 7.
ABC triangle mein B right angle hai, AC = 5 cm aur AB = 4 cm. O centre se ek circle draw kiya gaya hai OC radius ke saath. C aur B se passing chord ki length kya hogi?
(a) 3 cm
(b) 4 cm
(c) 5 cm
(d) 6 cm
Solution:
Right triangle ABC mein, ∠B = 90°
AC = 5 cm, AB = 4 cm

∴ BC² = AC² -AB²
= 5² – 4² = 25 – 16
= 9 = (3)²
∴ BC = 3 cm
∴ Chord BC ki length = 3 cm (a)

Question 8.
Agar AB, BC aur CD equal chords hain ek circle ke jiska centre O hai, aur AD diameter hai toh ∠AOB kya hoga?
(a) 60°
(b) 90°
(c) 120°
(d) none of these
Solution:
Circle mein chords AB = BC = CD

O circle ka centre hai
∴ ∠AOB = determine nahi kar sakte (d)

Question 9.
C arc AB ka mid-point hai ek circle ka jisme m(AB) = 183°. Agar region jo arc ACB aur line segment AB se bounded hai use S denote karte hain, toh centre O circle ka kaha lie karta hai?
(a) S ke interior mein
(b) S ke exterior mein
(c) segment AB par
(d) AB par aur AB ko bisect karta hai
Solution:
Arc AB = 183°
∴ AB circle ka diameter hai centre O ke saath aur C arc AB ka mid point hai

Line segment AB = S
∴ Centre AB par lie karega (c)

Question 10.
Ek circle mein, major arc minor arc se 3 times hai. Corresponding central angles aur degree measures kya honge?
(a) 90° aur 270°
(b) 90° aur 90°
(c) 270° aur 90°
(d) 60° aur 210°
Solution:
Circle mein, major arc = 3 times minor arc yani arc ACB = 3 arc ADB
∴ Reflex ∠AOB = 3∠AOB
Lekin angle at O = 360°

Agar ∠AOB = x
Toh reflex ∠ADB = x
x + 3x = 360°
⇒ 4x = 360°
⇒ x = 360°/4 = 90°
∴ 3x = 90° x 3 = 270°
Angles hain 270° aur 90° (c)

Question 11.
Agar A aur B circle ke do points hain jisme m(AB) = 260°. Arc BA ka angle jo circle ke kisi point par subtend hota hai, possible value kya ho sakti hai?
(a) 100°
(b) 75°
(c) 50°
(d) 25°
Solution:
A aur B circle ke do points hain jisme reflex ∠AOB = 260°

∴ ∠AOB = 360° – 260° = 100°
C circle ka ek point hai
∴ AC aur BC join karne par,
∠ACB = 1/2 ∠AOB = 1/2 x 100° = 50° (c)

Question 12.
Equilateral triangle ABC ek circle mein inscribed hai centre O ke saath. ∠BOC ka measure kya hai?
(a) 30°
(b) 60°
(c) 90°
(d) 120°
Solution:
∆ABC equilateral triangle hai jo circle mein inscribed hai centre O ke saath

∴ ∠BOC ka measure = 2∠BAC
= 2 x 60° = 120° (d)

Question 13.
Agar circle ke do diameters ek dusre ko right angles par intersect karte hain, toh unke end points ko join karne se bana quadrilateral kya hoga?
(a) rhombus
(b) rectangle
(c) parallelogram
(d) square
Solution:
Circle ke do diameter AB aur CD ek dusre ko right angles par intersect karte hain

AD, DB, BC aur CA join karke quadrilateral ABCD banta hai.
∵ Diagonals equal hain aur ek dusre ko right angles par bisect karte hain
∴ ACBD ek square hai (d)

Question 14.
ABC ek circle ka arc hai aur ∠ABC = 135°, toh arc AB ka ratio circumference ke saath kya hai?
(a) 1 : 4
(b) 3 : 4
(c) 3 : 8
(d) 1 : 2
Solution:
Arc ABC ek circle ka aur ∠ABC = 135°
OA aur OC join karte hain

∴ Arc ABC ka angle centre par = 2 x ∠ABC = 2 x 135° = 270°
Circle ke centre par angle = 360°
∴ Circumference ke saath ratio = 270° : 360° = 3:4 (b)

Question 15.
Circle ka chord uske radius ke equal hai. Ye chord minor arc par kya angle subtend karta hai?
(a) 60°
(b) 75°
(c) 120°
(d) 150°
Solution:
Circle ka chord = circle ka radius
Figure mein OA = OB = AB

∴ ∠AOB = 60°
(Equilateral triangle ka har angle = 60°) (a)

Question 16.
PQRS ek cyclic quadrilateral hai jisme PR circle ka diameter hai. Agar ∠QPR = 67° aur ∠SPR = 72°, toh ∠QRS kya hai?
(a) 41°
(b) 23°
(c) 67°
(d) 18°
Solution:
PQRS cyclic quadrilateral hai centre O ke saath aur ∠QPR = 67°
∠SPR = 72°

∴ ∠QPS = 67° + 72° = 139°
∵ ∠QPS + ∠QRS = 180° (Cyclic quadrilateral ke opposite angles ka sum)
⇒ 139° + ∠QRS = 180°
⇒ ∠QRS = 180° – 139° = 41° (a)

Question 17.
Agar A, B, C circle ke teen points hain centre O ke saath jisme ∠AOB = 90° aur ∠BOC = 120°, toh ∠ABC kya hai?
(a) 60°
(b) 75°
(c) 90°
(d) 135°
Solution:
A, B aur C circle ke teen points hain centre O ke saath
∠AOB = 90° aur ∠BOC = 120°

∴ ∠AOC = 360° – (120° + 90°)
= 360° -210°= 150°
Lekin ∠AOC centre par arc AC se bana hai aur ∠ABC circle ke remaining part par
∴ ∠ABC = 1/2 ∠AOC
= 1/2 x 150° = 75° (b)

Question 18.
Circle ka greatest chord kya kehlaata hai?
(a) radius
(b) secant
(c) diameter
(d) none of these
Solution:
Circle ka greatest chord uska diameter kehlaata hai. (c)

Question 19.
Circle ke minor segment mein bana angle kaisa hota hai?
(a) acute
(b) obtuse
(c) right angle
(d) none of these
Solution:
Circle ke minor segment mein bana angle obtuse angle hota hai. (b)

Question 20.
Teen non-collinear points se kitne circles draw ho sakte hain?
(a) 1
(b) 0
(c) 2
(d) 3
Solution:
Teen non-collinear points se sirf ek hi circle pass ho sakta hai. (a)

Question 21.
Figure mein, agar circle ke chords AB aur CD ek dusre ko right angles par intersect karte hain, toh x + y kya hai?
(a) 45°
(b) 60°
(c) 75°
(d) 90°

Solution:
Circle mein, AB aur CD do chords hain jo P par right angle par intersect karte hain yani ∠CPB = 90°

∠CAB aur ∠CDB same segment mein hain
∴ ∠CDB = ∠CAB = x
Ab triangle PDB mein,
External ∠CPB = ∠D + ∠DBP
⇒ 90° = x + y (∵ CD ⊥ AB)
Hence x + y = 90° (d)

Question 22.
Figure mein, agar ∠ABC = 45°, toh ∠AOC kya hai?
(a) 45°
(b) 60°
(c) 75°
(d) 90°

Solution:
∵ arc AC subtends
∠AOC centre par aur ∠ABC
circle ke remaining part par

∴ ∠AOC = 2∠ABC
= 2 x 45° = 90°
Hence ∠AOC = 90° (d)

Question 23.
Figure mein, chords AD aur BC ek dusre ko right angles par point P par intersect karte hain. Agar ∠DAB = 35°, toh ∠ADC kya hai?
(a) 35°
(b) 45°
(c) 55°
(d) 65°

Solution:
Do chords AD aur BC right angles par P par intersect karte hain, ∠DAB = 35°
AB aur CD join kiye gaye hain
Triangle ABP mein,
External ∠APC = ∠B + ∠A

⇒ 90° = ∠B + 35°
∠B = 90° – 35° = 55°
∵ ∠ABC aur ∠ADC same segment mein hain
∴ ∠ADC = ∠ABC = 55° (c)

Question 24.
Figure mein, O circle ka centre hai aur ∠BDC = 42°. ∠ACB ka measure kya hai?
(a) 42°
(b) 48°
(c) 58°
(d) 52°

Solution:
Figure mein, O circle ka centre hai
∠BDC = 42°
∠ABC = 90° (Semicircle mein angle)
aur ∠BAC aur ∠BDC circle ke same segment mein hain.
∴ ∠BAC = ∠BDC = 42°
Ab triangle ABC mein,
∠A + ∠ABC + ∠ACB = 180° (Triangle ke angles ka sum)

⇒ 42° + 90° + ∠ACB = 180°
⇒ 132° + ∠ACB = 180°
⇒ ∠ACB = 180° – 132° = 48° (b)

Question 25.
Centre O wale circle mein, AB aur CD do diameters hain jo ek dusre ke perpendicular hain. Chord AC ki length kya hai?

Solution:
AB aur CD circle ke do diameters hain centre O ke saath

Question 26.
Radius r ke do equal circles aise intersect karte hain ki har ek dusre ke centre se pass hota hai. Common chord ki length kya hai?

Solution:
Do equal circles ek dusre ke centre se pass hote hain aur A aur B par intersect karte hain
r har circle ka radius hai

Question 27.
Agar AB ek circle ka chord hai, P aur Q circle ke do points hain jo A aur B se different hain, toh kya relation hai?
(a) ∠APB = ∠AQB
(b) ∠APB + ∠AQB = 180° ya ∠APB = ∠AQB
(c) ∠APB + ∠AQB = 90°
(d) ∠APB + ∠AQB = 180°
Solution:
AB circle ka chord hai,
P aur Q do points hain A aur B ke alawa

∵ ∠APB aur ∠AQB circle ke same segment mein hain
∴ ∠APB = ∠AQB (a)

Question 28.
AB aur CD centre O wale circle ke do parallel chords hain jisme AB = 6 cm aur CD = 12 cm. Chords same side par hain centre ke aur unke beech distance 3 cm hai. Circle ka radius kya hai?

Solution:
AB aur CD centre O wale circle ke do parallel chords hain
r circle ka radius hai, AB = 6 cm, CD = 12 cm
aur unke beech distance = 3 cm
OC aur OA join karte hain, LM = 3 cm

OM = x maante hain, toh OL = x + 3

Question 29.
17 cm radius wale circle mein, do parallel chords diameter ke opposite sides par drawn hain. Chords ke beech distance 23 cm hai. Agar ek chord ki length 16 cm hai toh dusre ki length kya hai?
(a) 34 cm
(b) 15 cm
(c) 23 cm
(d) 30 cm
Solution:
Circle ka radius = 17 cm
Do parallel chords ke beech distance = 23 cm
AB || CD aur LM = 23 cm
OA aur OC join karte hain,
∴ OA = OC = 17 cm
OL = x maante hain, toh OM = (23 – x) cm
AB = 16 cm
Ab right triangle OAL mein,
OA² = OL² + AL²
⇒ (17)² = x² + AL²
⇒ 289 = x² + AL²

Question 30.
Figure mein, O circle ka centre hai jisme ∠AOC = 130°, toh ∠ABC kya hai?
(a) 130°
(b) 115°
(c) 65°
(d) 165°

Solution:
O circle ka centre hai aur ∠AOC = 130°
Reflex ∠AOC = 360° – 130° = 230°

Ab arc ADB centre par ∠AOC subtend karta hai aur circle ke remaining part par ∠ABC
∴ ∠ABC = 1/2 reflex ∠AOC
= 1/2 x 230°= 115° (b)

Ye sab solutions 2026 ke academic session ke liye updated hain. Hamare experts ne har question ko carefully solve kiya hai taaki students ko complete understanding mil sake. RD Sharma Class 9 Solutions Chapter 15 MCQs ko practice karne se students apne CBSE board exams mein better performance de sakte hain.

Chapter 15 “Areas of Parallelograms and Triangles” geometry ka important part hai. Ye MCQs students ko different types ke questions practice karne mein help karte hain. 2026 mein board exam pattern ke according, ye questions frequently asked jaate hain. Students ko chahiye ki wo regular practice karen aur har concept ko thoroughly understand karen.

In solutions ko access karne ke liye students ko koi special software ya app ki zarurat nahi hai. Ye solutions mobile-friendly hain aur kisi bhi device par easily access ho sakte hain. Students apne convenience ke according study kar sakte hain aur doubt clear kar sakte hain.

RD Sharma textbook CBSE board ke students ke liye highly recommended hai. Ye book comprehensive coverage provide karti hai aur step-by-step solutions students ki understanding improve karte hain. 2026 session ke liye updated content ensure karta hai ki students latest syllabus ke according prepare hoin.

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Complete RD Sharma Class 9 solutions ke liye students NCERT official website par bhi reference le sakte hain. Ye ensure karta hai ki students ko authentic aur updated information mile. 2026 mein success achieve karne ke liye consistent practice aur proper understanding zaroori hai.