Question

In the figure given below, PTis a tangent to the circle with centre O and PQ is the diameter though P.PR and QR are chords of the circle, If <RPT = 40", then find PQR​

Answer 1

Answer:

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=30

0

−∠QPT=90

0

−60

0

=30

0

In ΔPOQ

∠POQ=180−(∠OPQ+∠PQO)=180−30−30=120

0

Minor arc ∠POQ=120

0

Therefore Major arc ∠POQ=360

0

−120

0

=240

0

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

∴∠QRP=

2

1

∠POQ=120

0

Answer 2

Coreect Answer is angle PQR = 40°