Question

A point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.

Answer 1

by Using Pythagoras theorem

OP^2 = OT^2 + TP^2

(26)^2 = OT^2 + (10)^2

676 = OT^2 + 100

OT^2 = 676 - 100

OT^2 = 76

OT = 2√19

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Answer 2

Required Solution:

OP = 26 cm

• Given

PT = length of tαngent = 10 cm

rαdius = OT = ?

• To Find

We know that,

At point of contαct, rαdius αnd tangent are perpendiculαr ∠OTP = 90°

So, ∆OTP is right αngled triαngle.

Then by Pythαgorαs theorem, we hαve

OP² = OT² + PT²

26² = OT² + 10²

OT² = 676 – 100

OT = $\sf \sqrt{576}$

OT = 24 cm

Thus, OT = length of tαngent = 24 cm

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