Banner 0
Banner 1
Banner 2
Banner 3
Banner 4
Banner 5
Banner 6

Q.

In the adjoining figure, O is the centre of the circle and P, Q and R are points on the circle such that PQR= 100 ° ,   then OPR   equals:


Question Image

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away
An Intiative by Sri Chaitanya

a

80 °  

b

10 °  

c

100 °  

d

60 °   

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given that, O is the centre of the circle and P, Q and Rare points on the circle such that PQR= 100 ° .  
Question ImageHere, PR is chord we marks on major arc of the circle.
  PQRS is a cyclic quadrilateral.
So, the sum of opposite angles of cyclic quadrilateral PQRS is 180°  .
PQR+PSR= 180 °  
100+PSR= 180 °    PSR= 180 ° 100 °    PSR= 80 °  
We have to find the OPR  ,
Here, the arc PQR subtends PQR   at centre of a circle and PSR   on points.
So, the angle subtended by arc PQR at the centre is double the angle subtended by it at any other point on the circle.
POR=2PSR   POR=2× 80 ° POR= 160 °   Now,
In Δ   OPR, OP = OR (Radii of same circle arc equals)  OPR   = ORP   (Opposite angles to equal sides are equals) … (1)
Also, in ΔOPR  ,  OPR+ORP+POR= 180 °   (Angle sum property of triangle)  OPR+OPR+POR= 180 °       From (1),
2OPR+ 160 ° = 180 °    2OPR= 180 ° 160 °    2OPR= 20 °    OPR= 20 2    OPR= 10 °  
The value of OPR= 10 °  .
Hence, the correct option is 2.
 
Watch 3-min video & get full concept clarity

Best Courses for You

JEE

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

whats app icon
In the adjoining figure, O is the centre of the circle and P, Q and R are points on the circle such that ∠PQR= 100 ° ,   then ∠OPR   equals: