Question

From a point C, the length of the tangent to a circle is 8cm and the distance of Q from the center is 10cm. The radius of the circle is-
(a) 5cm
(b) 12cm
(c) 36cm
(d) 6cm​

Answer 1

Step-by-step explanation:

From a point C, the length of the tangent to a circle is 8cm and the distance of Q from the center is 10cm. The radius of the circle is- ( a) 5cm

Answer 2

Step-by-step explanation:

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,

AO2=AB2+OB2

(10)2=AB2+(8)2

⇒AB=100−64=6cm

Hence the length of tangent is 6cm.

Hence the correct answer is 6cm.