Same chapter4 marksDifficulty: Hard
In triangle ABC the bisector of angle A meets BC at D. Prove that BD/DC = AB/AC.
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4 marksDifficulty: Hard
In triangle ABC, right angled at B, BD is the perpendicular from B to AC. Prove that triangle ADB is similar to triangle ABC, and hence show that AB2 = AD × AC.
Original Khojo Papers practice question — not from a past board paper.
Answer
The triangles are similar by AA, and the proportion AD/AB = AB/AC gives AB2 = AD × AC.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
Angle A is common to both triangles and angle ADB = angle ABC = 90°, so the triangles are similar by the AA criterion. Corresponding sides are then proportional: AD/AB = AB/AC, which rearranges to AB2 = AD × AC.
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