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Question
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.
Options
BD = CD
BA > BD
BD > BA
CD > CA
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Solution
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then BA > BD.
Explanation:
Given, ∆ABC such that AD bisects ∠BAC
∴ ∠BAD = ∠CAD ...(i)
In ∆ACD, ∠BDA is an exterior angle.
∴ ∠BDA > ∠CAD [∵ Exterior angle > interior opposite angle] ...(i)
⇒ ∠BDA > ∠BAD ...[From equation (i)]
⇒ BA > BD ...[Side opposite to greater angle is greater]
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