In the figure, PQR and SQR are two right triangles with common hypotenuse QR. If
PR and SQ intersect at M, such that PM = 3cm, MR = 6cm and SM = 4cm, find the
value of MQ.
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In triangles PQS and PQR
∠P is common to both.
and ∠PSQ=∠PQR
Triangles PQS and PQR are equiangular
∴
PQ
PS
=
QR
QS
or, PS=
QR
PQ⋅QS
...(i)
Again, triangles QRS and PQR are equiangular
∴
QR
SR
=
PQ
QS
or, SR=
PQ
QS⋅QR
...(ii)
From eqns. (i) and (ii)
SR
PS
=
QR
PQ⋅QS
⋅
QR⋅QS
PQ
=
QR
2
PQ
2
I hope this is helpful for you
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