Question

O is the centre and seg PQ is a chord of a circle. <POQ=90° Radius OQ=28.Find the area of segment PRQ and PSQ​

Answer 1

Step-by-step explanation:

Given, PQ is a chord of a circle with center O. 

Also, ∠QPT=60°.

Let x be the point on the tangent PT.

∠QPT+∠OPT=90

⇒∠OPT=300−∠QPT=900−600=300

In ΔPOQ 

∠POQ=180−(∠OPQ+∠PQO)=180−30−30=1200

Minor arc ∠POQ=1200

Therefore Major arc ∠POQ=3600−1200=2400

Angle subtended by  an arc at centre is double the angle subtended by it on remaining part of circle

∴∠QRP=21∠POQ=1200