Question

from the
6. From appoint O. the length of the tangent to a circle is 24 cm and the distance of
centre of the circle is 25 cm. Find the radius of the circle
cm. Calculate the
7. The tangent to a circle of radius 6 cm from an external point P. is of length
distance of P from the nearest point of the circle.

Answer 1

Answer:

7 cm

Step-by-step explanation:

let the centre be A

AO is distance from center to point O = 25 cm

B be the point of contact of tangent

OB is length of tangent = 24 cm

as the tangent make 90° at point of contact with the radius.

we get a right angle triangle ABO

AB is the radius

by using Pythagoras theorem

${ao}^{2} = {ob}^{2} + {ab}^{2} \\ {25}^{2} = {24}^{2} + {ab}^{2} \\ 625 = 576 + {ab}^{2} \\ {ab}^{2} = 625 - 576 \\ {ab}^{2} = 49 \\ ab = \sqrt{49} \\ ab = 7$

therefore the radius of circle is 7 cm

hope you get your answer