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Question

In a triangle ABC, D and E are points on sides AB and AC respectively such that, DE||BC. Then ADAB =.

A
ACEC
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B
AEAC
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C
ECAE
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Solution

The correct option is B AEAC

Basic Proportionality Theorem says that if DE || BC, the ratio in
which point D divides AB is the same as the ratio in which point E divides AC.

The ratio in which D divides AB is given by ADDB. Similarly, the ratio in which E divides AC is given by AEEC.
ADDB=AEEC

Inverting the fraction and adding 1 on both sides
DB+ADAD=EC+AEAE

Now, we know AB=AB+DB and AE=AC+EC
Applying this in the above equation,
ABAD=ACAE

Hence, ADAB=AEAC

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