2026 · Q84
For the next three (03) items that follow : A circle with centre O passes through the vertex A of an equilateral triangle ABC and touches BC at its midpoint M. The circle cuts AB at D and AC at E. What is AD : DB equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A2 : 1
- B3 : 2
- C3 : 1
- D4 : 3
Explanation
By the tangent-secant theorem at B, BM² = BD·BA. Since M is the midpoint of BC, BM = s/2 for triangle side s, so (s/2)² = BD·s gives BD = s/4. Then AD = s − s/4 = 3s/4 and AD : DB = 3 : 1, option C.