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Geometry Area of Triangle with Inscribed Circle

XAT 2015 · Quantitative Ability & Data Interpretation · Hard · Quantitative Ability

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The centre of a circle inside a triangle is at a distance of 625 cm625\text{ cm} from each of the vertices of the triangle. If the diameter of the circle is 350 cm350\text{ cm} and the circle is touching only two sides of the triangle, find the area of the triangle.

  1. A.

    240000

  2. B.

    387072

  3. C.

    480000

  4. D.

    506447

  5. E.

    None of the above

Answer

B

Explanation

Since the center SS is at distance 625625 from all three vertices, SS is the circumcenter. Radius of circle r=350/2=175r = 350 / 2 = 175. Distance AR=6252−1752=600AR = \sqrt{625^2 - 175^2} = 600. Calculating altitude and base segments, area =△ASB+△ASC+△SBC=105000+105000+177072=387072 sq.cm= \triangle ASB + \triangle ASC + \triangle SBC = 105000 + 105000 + 177072 = 387072\text{ sq.cm}.

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