AB is a diameter of a circle with center O. CB is a tangent to the circle at B. AC intersects the circle at G. If the radius of the circle is 8 cm and AG = 12 cm, then the length of BC is?
Answer & explanation
Correct answer: option 1
In Δ ABG,
AB = 2 × 8 = 16,
AG = 12 and ∠AGB = 90°, therefore,
BG = \(\sqrt {16^2 - 12^2}\) = \(\sqrt {256 - 144}\) = \(\sqrt {112}\) = 4\(\sqrt {7}\)
BC = \(\frac{AB × BG}{AG}\) = \(\frac{16 × 4\sqrt {7}}{12}\)
= \(\frac{16\sqrt {7}}{3}\)