Using Apollonius theorem, find the median.

6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

7

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

9

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is B $9$
According to the Apollonius theorem,
$A B^{2} + A C^{2} = 2 [A D^{2} + {\frac{B C}{2}}^{2}]$
$8^{2} + 10^{2} = 2 [A D^{2} + {\frac{2}{2}}^{2}]$
$64 + 100 = 2 [A D^{2} + 1]$
$2 A D^{2} = 164 - 2$
$2 A D^{2} = 162$
$A D^{2} = \frac{162}{2}$
$A D^{2} = 81$
$A D = 9$
$A D =$ Median $= 9$

Suggest Corrections

Similar questions

Δ

A B C, A C = 8, B C = 2, A B = 6

A D

△ A B C, ¯ ¯¯¯¯¯¯¯ ¯ A D

Which of the following theorems is a prerequisite for proving Apollonius Theorem?

A D

△ A B C

= 5

x	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
f	$9$	$11$	$5$	$6$	$8$	$1$	$3$	$7$

Join BYJU'S Learning Program