The perpendicular from A on side BC of a - ABC intersect B C at D such that D B-3 C D - Prove that 2 A B2-2 A C2-B C2

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Pythagoras Theorem

The perpendic...

Question

The perpendicular from A on side BC of a ΔABC intersect BC at D such that DB = 3 CD. Prove that 2 AB² = 2 AC² + BC²

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Δ A B C

2 A B^{2} = 2 A C^{2} + B C^{2}

A

B C

B C

D

D B = 3 C D

2 A B^{2} = 2 A C^{2} + B C^{2}

Δ A B C

2 A B^{2} = 2 A C^{2} + B C^{2}

A D

B C

△ A B C

B C

D

D B = 3 C D

2 {A B}^{2} = 2 {A C}^{2} + {B C}^{2}

△ A B C

D B = 3 \times C D

2 {A B}^{2} = 2 {A C}^{2} + {B C}^{2}

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