2014 · Q69
ABC is a triangle right-angled at A where AB = 6 cm and AC = 8 cm. Semicircles are drawn (outside the triangle) on AB, AC and BC as diameters which enclose areas x, y and z square units respectively. What is x + y - z equal to?
Elementary MathematicsGeometry
- A48 cm^2
- B32 cm^2
- C0
- DNone of the above
Explanation
By Pythagoras, x + y - z = (π/8)(36 + 64 - 100) = 0 (lunes theorem).