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Question

State true or false:

In triangle ABC, P is the mid-point of side BC. A line through P and Parallel to CA meets AB at point Q; and a line through Q and parallel to BC meets median AP at point R. Can it be concluded that,
AP=2AR ?

A
True
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B
False
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Solution

The correct option is A True
Given: ABC, P is mid point of BC, QRBC and PQAC
Since, PQAC and P is mid point of BC, thus, by converse of mid point theorem
Q is mid point of AB.
Now, In ABP
Since, QRBP and Q is mid point of AB. thus, by converse of Mid point theorem
R is mid point of AP.
Hence, AP=2AR

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