You visited us 1 times! Enjoying our articles? Unlock Full Access!

The Mid-Point Theorem

In ABC, poi...

Question

In $△ A B C$ , point $M$ is the midpoint of side $B C$ . If $A B^{2} + A C^{2} = 290 c m^{2}, A M = 8 c m$ , find $B C$ .

Open in App

Solution

Formula: Apollonius's theorem

Given,

$A B^{2} + A C^{2} = 290, A M = 8$

$A B^{2} + A C^{2} = 2 (A M^{2} + B M^{2})$

$290 = 2 (8^{2} + B M^{2})$

$145 = 64 + B M^{2}$

$\Rightarrow B M = 9$ cm

$B C = B M + M C$

$= 2 B M$

$= 2 \times 9$

$= 18$ cm

Suggest Corrections

Similar questions

A D

A B C

A M ⊥ B C

A C^{2} = A D^{2} + B C . D M + {(\frac{B C}{2})}^{2}

A B^{2} = A D^{2} B C . D M + {(\frac{B C}{2})}^{2}

A C^{2} + A B^{2} = 2 A D^{2} + \frac{1}{2} B C^{2}

△ A B C

A B^{2} + A C^{2} = 122

10

△ A B C

D

B C .

A B^{2} + A C^{2} = 2 (. . . . . . . . . . . .)

△ A B C

A P

A P = 7

{A B}^{2} + {A C}^{2} = 260

B C

Join BYJU'S Learning Program