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Question

A circle touches sides AD and CD of rectangle ABCD at P and Q, respectively. If the length of the perpendicular from B to PQ is 10 units, then area of rectangle is
296596_139be5df6116436da9f9c14f40198768.png

A
25
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B
50
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C
75
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D
100
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Solution

The correct option is D 100
Given, BE=10
AD and DC touches the circle
BPQ=BQC
and APB=PQB
also BQC and EPB are similar
and APB and EQB are similar
BCBE=BQBP=BEABAB×BC=(BE)2=(10)2=100

888432_296596_ans_bbc702b5469a4615bca61d905dc22e50.png

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