Question

In the diagram of circle K, tangents are drawn from point A to points B and C on the circle. If mBC=96, then what is the measure of angle A. Show how you arrived at your answer.

Answer 1

∠ A = 84°

Explanation:

The measure of the tangent- tangent angle A is half the difference of the intercepted arcs.

major arc BC = 360° - 96° = 264°, thus

∠ A =
`(1)/(2)` (264 - 96)° =
`(1)/(2)` × 168° = 84°