Question

In the following circle, m∠BOC=120°. Find PBC.

Answer 1

See Explanation

Explanation:

`m\angle BOC= 120\degree.... (Given)`

Since, measure of minor arc is equal to the measure of the central angle.

`\therefore m\widehat {BC} = m\angle BOC\\\\</p><p>\therefore m\widehat {BC} =120\degree \\\\</p><p>\because m\angle PBC = (1)/(2) * m\widehat {BC}\\(By\: tangent\: secant\: theorem) \\</p><p>\huge\purple{\boxed {\therefore m\angle PBC =60\degree}} \\\\`

Since, AC is the diameter of the circle.

`\therefore m\widehat {AB} +m\widehat {BC} = 180\degree \\\\</p><p>\therefore m\widehat {AB} +120\degree = 180\degree \\\\</p><p>\therefore m\widehat {AB} = 180\degree - 120\degree\\\\</p><p>\huge\orange {\boxed {\therefore m\widehat {AB} = 60\degree}}`