Indian Institute of Foreign Trade 2008 Solved Paper

Question : 58 of 150

Marks: +1, -0

If D is the midpoint of side BC of a triangle ABC and AD is the perpendicular to AC then:

Solution:

Using Apollonius theorem in ∆ABC, we can say that

2(AD^2+BD^2)=AB^2+AC^2

In right-angle triangle ADC

DC^2=AD^2+AC^2

....(2)
By equation (1) and (2), we can say that

2(DC^{2}-AC^{2}+BD^{2})=AB^{2}+AC^{2}

3AC^2=BC^2−AB^2

Therefore, option A is the correct answer.

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