Question

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is?

Answer 1

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Let O be center, OP be radius.

Applying Pythagoras

PQ = 24, OQ = 25

OQ^2 = OP^2 + PQ^2

25^2 = OP^2 + 24^2

625 = OP^2 + 576

OP^2 = 49

OP = 7 cm

Radius of Circle = 7 cm

Answer 2

Answer:

The radius of circle is 7cm.

Step-by-step explanation:

Solution:-

Consider O as center P and Q are. the point in the tangent line.

P is the point of contact.

XY is the tangent line.

PQ = 24cm

OQ = 25cm

From the above data, draw a diagram.

XY is the tangent line

OP ⏊ XY

so, ∠OPQ = 90°

Now, applying Pythagoras theorem

(Hypotenuse)^2 = (Height)^2 + (Base)^2

(OQ)^2 = (OP)^2 + (PQ)^2

→ (25)^2 = (OP)^2 + (24)^2

→ (OP)^2 = (25)^2 - (24)^2

→ (OP)^2 = 625 - 576

→ (OP)^2 = 49

→ OP = √(49)

→ OP = 7cm

Therefore, the radius of circle is 7cm.