Question


Q20)PQ is a chord of a circle with centre O. PQ=25. M is a point on the chord PQ such that PM=9cm and d(OM)=5cm. Then radius of circle= ______.

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Circles

Equal Chords

In the following figure, PQ...

MATHS

In the following figure, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT=60

o

, find ∠PRQ.

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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

solution