2021 · Q83
Consider the following for the next three (03) items that follow : ABC is a triangle with sides AB = 6 cm, BC = 10 cm and CA = 8 cm. With vertices A, B and C as centres, three circles are drawn each touching the other two externally. If P, Q and R are the areas of sectors at A, B and C within the triangle respectively, then which of the following is/are correct ?
- 1P = π cm².
- 29Q + 4R = 36π cm².
Select the correct answer using the code given below:
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Solving the tangency system gives r_A = 2, r_B = 4, r_C = 6 cm, and angle A = 90°. Statement 1: P = (90/360)π(2²) = π ✓. Statement 2: 9Q + 4R = 9·(B/360)π·16 + 4·(C/360)π·36 = (144/360)(B+C)π = (144/360)·90°·π = 36π ✓. Both are correct, option (c).