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Question

P is the mid-point of side AB to a parallelogram ABCD. A line through B parallel to PD meets DC at Q and AD produced at R. Then BR is equal to ______.
315091_61c3bb786b9847b98053d94fdefeab93.png

A
BQ
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B
12BQ
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C
2BQ
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D
None of these
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Solution

The correct option is C 2BQ
In ABR, P is the mid-point of AB and DP||BR
D is the mid-point of AR .....(Converse of mid-point theorem).
Then, AR=2AD
AR=2BC (Opposite sides of parallelogram are equal, i.e. AD=BC)
AD=BC.

Also, D is the mid-point of AR and DQ||AB ....(Since, ABCD is parallelogram)
Then, Q is the mid-point of DC ....(Converse of mid-point theorem)
BR=2BQ.

Hence, option C is correct.

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