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16. In AABC, if ADBC and AD2-BD x DC provethat LBAC = 90°.

Answer»

In triangle ABC , AD is perpendicular to BC and AD² = BD.DC

To prove : BAC = 90°

Proof : in right triangles ∆ADB and ∆ADCSo, Pythagoras theorem should be apply , Then we have , AB² = AD² + BD² ----------(1)AC²= AD²+ DC² ---------(2)

AB² + AC² = 2AD² + BD²+ DC²= 2BD . CD + BD² + CD² [ ∵ given AD² = BD.CD ] = (BD + CD )² = BC²Thus in triangle ABC we have , AB² + AC²= BC²

hence triangle ABC is a right triangle right angled at A

∠ BAC = 90°



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