In the figure given below, PT is a tangent to the circle with centre O and PQ is the diameter through P. PR and QR are chords of the circle . If angle RPT= 40 degree, then find angle PQR.
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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
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