2019 · Q65
Consider a trapezium ABCD, in which AB is parallel to CD and AD is perpendicular to AB. If the trapezium has an incircle which touches AB at E and CD at F, where EB = 25 cm and FC = 16 cm, then what is the diameter of the circle?
Elementary MathematicsQuadrilaterals and Polygons
- A16 cm
- B25 cm
- C36 cm
- D40 cm
Explanation
Tangent lengths from B total 25+25 and from C total 16+16 along BC, so BC = 41. With the incircle centre at (r,r), B = (r+25,0), C = (r+16,2r): BC^2 = 81+4r^2 = 1681 gives r = 20. Diameter = 40 cm.