Question

In the figure below, PQ and RS are equal chords of a circle with centre T.
What is the measure of angle PTQ ?
PQ = RS
​

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