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Question
In the given figure, ABCD is a trapezium. P and Q are the midpoints of non-parallel side AD and BC respectively. Find: DC, if AB = 20 cm and PQ = 14 cm
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Solution
Let us draw a diagonal AC which meets PQ at O as shown below:
Given AB = 20 cm and PQ = 14 cm
In ΔABC,
OQ = `(1)/(2)"AB"` ....(Mid-point Theorem)
⇒ OP = `(1)/(2) xx 20` = 10 cm
Now,
OP = PQ - OQ
⇒ OP = 14 - 10
= 4 cm
In ΔADC,
OP = `(1)/(2)"DC"` ....(Mid-point Theorem)
⇒ DC = 2 x OP
= 2 x 4
= 8 cm.
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