ABC is right Δ, right angled at C and D is the mid point of BC. Prove that AC²=4AD²-3AB².

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Solution

triangle ABC is a right angled triangle right angled at C and D is the mid point of bc .
by applying pythagoras theorem in triangle ABC , we get
AB²=AC²+BC²
=AC²+(2CD)²(SINCE D IS THE MID POINT OF BC)
=AC²+4CD²
=AC²+4(AD^2_AC²)
( SINCE IN TRIANGLE ACD WE GET AD²=AC²+CD²) =AC²+4AD^2_4AC^2
=4AD^2_3AC²
THEREFORE , AB²=4AD^2_3AC².

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ABC is a right angled triangle at C. If D is the mid point of BC,prove that AB²=4AD²-3AC²

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