2026 · Q82
For the next three (03) items that follow : The centre O of a circle inside a triangle ABC is at a distance of 13 cm from each of the vertices of the triangle. The diameter of the circle is 10 cm and the circle touches only two sides of the triangle, AB and AC. If y is the area in cm² of the triangle, then which one of the following is correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A190 cm² < y < 200 cm²
- B200 cm² < y < 210 cm²
- C210 cm² < y < 220 cm²
- D220 cm² < y < 230 cm²
Explanation
From the previous question's setup, b = c = 24 and sin A = 120/169. The triangle's area is y = ½·b·c·sin A = ½·24·24·(120/169) = 34560/169. Numerically this is about 204.5 cm², which lies in (200, 210), option B.