Question

1. A tangent of length 24cm is drawn to a circle from a point 25cm from its centre.
Find the radius of the circle​

Answer 1

Answer:

Let O be the centre of the circle.

Given that,

OQ = 25cm and PQ = 24 cm

As the radius is perpendicular to the tangent at the point of contact,

Therefore, OP ⊥ PQ

Applying Pythagoras theorem in ΔOPQ, we obtain

OP2 + PQ2 = OQ2

OP2 + 242 = 252

OP2 = 625 − 576

OP2 = 49

OP = 7

Therefore, the radius of the circle is 7 cm.

Step-by-step explanation:

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Answer 2

Given:

OP = 25 cm

PT = 24 cm

Find:

Radius.

Solution:

Let O be the center of circle, OP = 25 cm

Let T be the any point on the circle, then PT = 24 cm

From Figure: OT ⊥ PT In right ∆OPT,

By Pythagoras Theorem:

OP2 = OT2 + PT2

252 = OT2 + (24)2

625 = OT2 + 576

OT = 7

Radius of the circle is 7 cm.

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