Answer:
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)
