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Question
D is any point on side AC of a ∆ABC with AB = AC. Show that CD < BD.
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Solution
Given in triangle ABC, D is any point on side AC such that AB = AC.
To proof that CD < BD or BD > CD
To proof: AC = AB ...[Given]
∠ABC = ∠ACB ...(i) [Angle opposite to equal sides are equal]
In triangle ABC and triangle DBC,
∠ABC > ∠DBC ...[∠DBC is a internal angle of ∠B]
∠ACB > ∠DBC ...[From equation (i)]
BD > CD ...[Side opposite to greater angle is longer]
CD < BD
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