Question

if the tangent at point P to a circle with center O cut a line through O at P such that PQ=24 cm and OQ= 25cm, find the radius of the circle​

Answer 1

Refer to the attachment

$\large \tt Question$

If the tangent at point P to a circle with center O cut a line through O at P such that PQ=24 cm and OQ= 25cm, find the radius of the circle.

$\large\frak \pink{Answer}$

$= \colorbox{lime}{ \bf7 \: cm}$

$\huge \tt Solution$

In the above diagram shown a tangent PQ at a point P which cuts off the radius of the circle OP

having a centre O.

Now , PQ = 24 cm

OQ = 25 cm

we know that

$\sf \: PQ \perp OP$

OP² = OP² + PQ²

25² = r² + 24²

r = 7 cm

Conclusion

The radius of circle = 7 cm

Thankyou

Answer 2

Answer:

Since QT is a tangent to the circle at T and OT is radius,

Therefore OT perpendicular QT It is given that OQ=25 cm and QT= 24 cm

By Pythagoras theorem we have

$ob ^{2} = {oa}^{2} + {ab}^{2} \\ {oq}^{2} = {qt}^{2} + {ot}^{2} \\ {ot}^{2} = {25}^{2} + {24}^{2} \\ = 49 \times 1 = 49 \\ ot = 7$