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Question
In ΔABC, angle ABC is equal to twice the angle ACB, and bisector of angle ABC meets the opposite side at point P. Show that: CB : BA = CP : PA
Solution
In ΔABC,
∠ABC = 2∠ACB
Let ∠ACB = x
`=>` ∠ABC = 2∠ACB = 2x
Given BP is bisector of ∠ABC
Hence ∠ABP = ∠PBC = x
Using the angle bisector theorem,
That is the bisector of an angle divides the side opposite to it in the ratio of other two sides.
Hence, CB : BA = CP : PA.
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