2019 · Q84
In a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC?
Elementary MathematicsCircles
- A2√6 cm
- B3√6 cm
- C3√7 cm
- D6√7 cm
Explanation
Let M be where OA meets BC, OM = d. Then BM^2 = 64−d^2 and AM^2 = 144−BM^2 = 80+d^2, while AM = 8±d. This gives d = ±1, so BM = √63 = 3√7 and BC = 6√7 cm.