Triangle ABC is a right angled at A The points P and Q are
on hypotenuse BC such that BP = PQ = QC.If AP = 3 and AQ=4 Then, Find BC= ?
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BP=PQ=QC=x(let)
AP=3;AQ=4
In△AQB
APismedianbyApolloniusThmAB
2
+AQ
2
=2(AP
2
+PQ
2
)
⟹AB
2
+16=2(9+x
2
)
⟹AB
2
=2x
2
+2−(1)
Similarly,in△APC
AQismedian
So,
AC
2
+AP
2
=2(AQ
2
+QC
2
)
∴AC
2
+9=2(16+x
2
)
⟹AC
2
=2x
2
+23−(2)
(1)+(2)
AB
2
+AC
2
=4x
2
+25
⟹BC
2
=4x
2
+25[In△ABC,usingpythagorasthm]
⟹(3x)
2
=4x
2
+25
⟹9x
2
=4x
2
+25
⟹x=
5
BC=3x=
45
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