AD is perpendicular to BC,if BD/AD=DA/DC,prove that triangle ABC is a right triangle

Asked by  | 21st Sep, 2013, 07:44: PM

Expert Answer:

In right triangles ADB & ADC, we have:

AB2 = AD+BD. . . . . . . . .1

AC= AD2+ DC2 . . . . . . . . 2

From 1 & 2,

AB2 + AC2 = 2AD2 + BD2 + DC2

= 2BD . CD + BD2 + CD2 [Given: AD*2 = BD . CD]

= (BD + CD)2 = BC2

Thus, in triangle ABC we have , AB2 + AC2 = BC2

Hence, triangle ABC is a right triangle right angled at A.

Answered by  | 22nd Sep, 2013, 02:15: PM

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