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Question: If the radius of the circumcircle of an isosceles triangle PQR is equal to PQ (= PR), then the angle...

If the radius of the circumcircle of an isosceles triangle PQR is equal to PQ (= PR), then the angle P is –

A

π/6

B

π/3

C

π/2

D

2π/3

Answer

2π/3

Explanation

Solution

Circum radius R = PQ = PR

∴ PQ = PR = = =

⇒ sin R = sin Q = 12\frac { 1 } { 2 } ⇒ ∠R = ∠Q = π6\frac { \pi } { 6 } 

⇒ ∠P = π – ( < R + < Q) = 2π3\frac { 2 \pi } { 3 }