Question

A triangle PQR where PQ=QR and angle Q=60 is inscribed in a circle . If S is any point in minor arc QR but not coincide with Q and R then prove that PS bisects angle QSR

Answer 1

PS bisects ∠QSR  in A triangle PQR where PQ=QR and angle Q=60 is inscribed in a circle

Step-by-step explanation:

A triangle PQR where PQ=QR and angle Q=60

PQ = QR

=> ∠Q = ∠R

=> ∠R = 60°

∠P + ∠Q + ∠R = 180°

=> ∠P = 60°

Hence PQR is an equilateral triangle

=> PQ = PR = QR

PS will create two angle

∠PSQ   &  ∠PSR

if PS bisects ∠QSR

then ∠PSQ   = ∠PSR

∠PSQ is angle subtended by chord PQ at arc segment

∠PSR is angle subtended by chord by PR at arc segment

PQ = PR

Angle subtended by equal length chord are equal

hence  ∠PSQ   = ∠PSR

Hence  PS bisects ∠QSR

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Answer 2

Answer:

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