2026 · Q36
ABC is a triangle right-angled at C. A semicircle is drawn on AB as diameter. Let P be any point on AC produced such that AP = AB = 10 cm. Further, B and P are joined. If BC = 8 cm, then what is BP equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A4√5 cm
- B9 cm
- C10 cm
- D5√5 cm
Explanation
With ∠C=90°, AB=10 and BC=8, Pythagoras gives AC=6. Since P lies on AC produced with AP=10, CP=10−6=4 and ∠PCB=90°. Hence BP=√(8²+4²)=√80=4√5 cm, option A.