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

Step-by-step explanation: x=-2,2...

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

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mackenzie112068

07.02.2022

Mathematics

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Step-by-step explanation:

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

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

$\therefore m\widehat {BC} = m\angle BOC\\\\\therefore m\widehat {BC} =120\degree \\\\\because m\angle PBC = \frac{1}{2} \times m\widehat {BC}\\(By\: tangent\: secant\: theorem) \\\huge\purple{\boxed {\therefore m\angle PBC =60\degree}} \\\\$

Since, AC is the diameter of the circle.

$\therefore m\widehat {AB} +m\widehat {BC} = 180\degree \\\\\therefore m\widehat {AB} +120\degree = 180\degree \\\\\therefore m\widehat {AB} = 180\degree - 120\degree\\\\\huge\orange {\boxed {\therefore m\widehat {AB} = 60\degree}}$

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

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