Question

9. If radius of circle is 8 cm and tangent is drawn from an external point to
the circle is 15 cm, find the distance from centre of circle to the external
point​

Answer 1

Given:- A circle with center O and AB is the tangent from point A.

Radius of circle =OB=8cm

Distance of point from the circle =AO=10cm

To find:- Length of tangent, i.e., AB=?

Solution:-

Since AB is tangent,

Therefore,

AB⊥OB[∵Tangent at any point of circle is perpendicular to the radius through point of contact]

⇒∠ABO=90°

Hence △OAB is a right angle triangle.

Using pythagoras theorem in △OAB,

AO

2

=AB

2

+OB

2

(10)

2

=AB

2

+(8)

2

⇒AB=

100−64

=6cm

Hence the length of tangent is 6cm.

Hence the correct answer is 6cm.