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Question

In the above figure, if RB, SC and TO are perpendiculars to BD with the length indicated, then xy is equal to
371133.png

A
pq
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B
pp+q
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C
qp
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D
qp+q
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Solution

The correct option is A pq
In triangles RBD and SCD
D is common to both.
and B=C (because each angle is right angle)
Triangles
RBD and SCD are equiangular
RBSC=BDCD
or, xz=p+qq
Similarly triangles TDB and SCB are equiangular
SCTD=BCBD
or, zy=qp+q
xz×zy=p+qq×pp+q
xy=pq

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