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Question: Answered & Verified by Expert
ABCD is a trapezium such that AB and CD are parallel and BCCD. If ADB=θBC=p and CD=q, then AB is equal to
MathematicsHeights and DistancesJEE MainJEE Main 2013 (07 Apr)
Options:
  • A p2+q2p2cosθ+q2sinθ
  • B p2+q2sinθpcosθ+qsinθ2
  • C p2+q2sinθpcosθ+qsinθ
  • D p2+q2cosθpcosθ+qsinθ
Solution:
2836 Upvotes Verified Answer
The correct answer is: p2+q2sinθpcosθ+qsinθ

Let BDC=α, then

tanα=BCCD=pq

AE=BC=p

tanα+θ=AEED

ED=ptanα+θ

=p1-tanαtanθtanα+tanθ

=p1-pqtanθpq+tanθ

Now, AB=q-ED

=q-pq-ptanθpq+qtanθ

=pq+q2tanθ-pq+p2tanθp+qtanθ

=p2+q2tanθp+qtanθ

=p2+q2sinθpcosθ+qsinθ

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