A and B are centres of two circles of radii 8 cm and 1 cm such that AB = 13 cm and angle ACB = 90 degree where C is the centre of another circle which touches the above two circles. Find the area of the circle with centre C

50.28 sq. cm.

Step-by-step explanation:

A and B are centers of two circles of radii 8 cm and 1 cm such that AB = 13 cm.

Now, angle ACB = 90 degree where C is the center of another circle which touches the above two circles.

Now, ABC forms a right triangle where AB = 13 cm, AC = (r + 8) cm and BC = (1 + r) cm.

{Where r is the radius of the circle C.

Applying Pythagoras Theorem. AB² = AC² + BC²

⇒ 13² = (r + 8) ² + (r + 1) ²

⇒ 169 = r² + 16r + 64 + f² + 2r + 1

⇒ 2r² + 18r - 104 = 0

⇒ r² + 9r - 52 = 0

⇒ (r + 13) (r - 4) = 0

Hence, r = 4 {As the value of r can not be negative}

Therefore, the area of the circle C is π (4) ² = 50.28 sq. cm. (Answer)