Question

The centre of a circle inside a triangle is at a distance of $625	ext{ cm}$ from each of the vertices of the triangle. If the diameter of the circle is $350	ext{ cm}$ and the circle is touching only two sides of the triangle, find the area of the triangle.

Accepted Answer

B. Since the center $S$ is at distance $625$ from all three vertices, $S$ is the circumcenter. Radius of circle $r = 350 / 2 = 175$. Distance $AR = \sqrt{625^2 - 175^2} = 600$. Calculating altitude and base segments, area $= 	riangle ASB + 	riangle ASC + 	riangle SBC = 105000 + 105000 + 177072 = 387072	ext{ sq.cm}$.

Geometry Area of Triangle with Inscribed Circle

Explanation

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