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In ∆Abc Seg Ap is a Median. If Bc = 18, Ab2 + Ac2 = 260 Find Ap. - Geometry

ConceptApollonius Theorem

Question

In ∆ABC seg AP is a median. If BC = 18, AB2 + AC2 = 260 Find AP.

Solution

In ∆ABC, point P is the midpoint of side BC.

$BP = PC = \frac{1}{2}BC = 9$
${AB}^2 + {AC}^2 = 2 {AP}^2 + 2 {BP}^2 \left( \text{by Apollonius theorem} \right)$
$\Rightarrow 260 = 2 {AP}^2 + 2\left( 9^2 \right)$
$\Rightarrow 260 = 2 {AP}^2 + 2\left( 81 \right)$
$\Rightarrow 260 = 2 {AP}^2 + 162$
$\Rightarrow 2 {AP}^2 = 260 - 162$
$\Rightarrow 2 {AP}^2 = 98$
$\Rightarrow {AP}^2 = 49$
$\Rightarrow AP = 7$

Hence, AP = 7.

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APPEARS IN

Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 2: Pythagoras Theorem
Problem Set 2 | Q: 6 | Page no. 44
Solution In ∆Abc Seg Ap is a Median. If Bc = 18, Ab2 + Ac2 = 260 Find Ap. Concept: Apollonius Theorem.
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