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

Apollonius's Theorem

In ABC, AP ...

Question

In $△ A B C$ , AP is the median. If $A P = 7$ and $A B^{2} + A C^{2} = 260$ , then find BC.

14

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

18

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

15

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

12

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

Open in App

Solution

The correct option is D $18$ cm
By Apollonius Theorem (states that "the sum of the squares of any two sides of any triangle equals twice the square on half the third side, together with twice the square on the median bisecting the third side".) , we have

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

$B C^{2} = 260 + 2 (7)^{2}$

$B C^{2} = 260 + 98 = 358$

$B C = 18.92$

Suggest Corrections

Similar questions

△ A B C

A P

A P = 7

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

B C

△ A B C

A P

B C = 18, A B^{2} + A C^{2} = 260

The area of following triangle is 30 cm². If BC = 5 cm then AP = ?

Δ A B C

A P

A P = 12, A B^{2} + A C^{2} = 320

B P

Join BYJU'S Learning Program