2023 · Q91
Consider the following for the next three (03) items that follow: In triangle ABC, AB = 6 cm, BC = 8 cm and AC = 10 cm. The perpendicular dropped from B meets the side AC at D. A circle of radius BD (with centre B) cuts AB and BC at P and Q respectively. What is the length of QC?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A4.4 cm
- B4.2 cm
- C3.6 cm
- D3.2 cm
Explanation
6² + 8² = 10², so the triangle is right-angled at B. The altitude BD = 6·8/10 = 4.8 cm is also the circle's radius, meeting BC at Q with BQ = 4.8. Hence QC = 8 − 4.8 = 3.2 cm (D).