The correct answer is option (B):
49π cm2
Let's break this problem down step by step. We need to find the area of a circle, and we know its radius is related to the inradius of a given triangle.
First, let's check if the triangle is a right-angled triangle. We can use the Pythagorean theorem: a² + b² = c², where c is the longest side (the hypotenuse).
In this case, the sides are 15 cm, 8 cm, and 17 cm.
8² + 15² = 64 + 225 = 289
17² = 289
Since 8² + 15² = 17², the triangle is a right-angled triangle.
Now, we need to find the inradius (r) of the triangle. For a right-angled triangle, the inradius can be calculated using the formula: r = (a + b - c) / 2, where a and b are the legs and c is the hypotenuse.
So, r = (8 + 15 - 17) / 2 = (23 - 17) / 2 = 6 / 2 = 3 cm.
The radius of the circle is given as (r + 4) cm. Since r = 3 cm, the circle's radius is (3 + 4) = 7 cm.
The area of a circle is calculated using the formula: Area = π * radius²
Therefore, the area of the circle is π * 7² = 49π cm².
The correct answer is 49π cm².