In an equalateral ∆PQR,M is a point on side QR.Such that QM=1/3QR prove that 9PM^2=7PQ^2
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Step-by-step explanation:
Correct option is
D
2
3
a
In the figure AP⊥BC
AB=BC=CA=a
In △APB and △APC
∠APB=∠APC=90
∘
∠ABP=∠ACP−60
∘
(ABC is equilateral triangle)
By AA similarity
△APB∼△APC
∴
AP
AP
=
PC
PB
=
AC
AB
⇒
PC
PB
=1⇒PB=PC
⇒PB+PC=a
⇒2PB=a
⇒PB=
2
a
In △APB,∠APB=90
∘
AB
2
=AP
2
+PB
2
⇒a
2
=AP
2
+(
2
a
)
2
⇒AP
2
=a
2
−
4
a
2
⇒AP
2
=
4
3a
2
⇒AP=
2
3
a
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