In right-angled triangle ABC is which ∠C = 90°, if D is the mid-point of BC, prove that AB² = 4 AD² − 3AC².

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Solution

∆ABC is a right-angled triangle with ∠C = 90°. D is the mid-point of BC.

We need to prove that.
Join AD.

Since D is the midpoint of the side BC, we get

BD = DC

∴

Using Pythagoras theorem in triangles right angled triangle ABC

.....(1)

Again using Pythagoras theorem in the right angled triangle ADC

.....(2)

From (1) and (2), we get

Hence, .

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Similar questions

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

Δ

B C^{2} = 4 (A D^{2} - A C^{2})

∠ B = 90^{\circ}

B C

D

E

8 {A E}^{2} = 3 {A C}^{2} + 5 {A D}^{2}

△ A B C, ∠ A C B = 90^{\circ}

{A B}^{2}

{4 A D}^{2} - {3 A C}^{2}

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