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Any Point Equidistant from the End Points of a Segment Lies on the Perpendicular Bisector of the Segment

In a Δ ABC, i...

Question

In a $Δ$ ABC, it is given that AB = AC and AD is drawn perpendicular to BC. D is not the mid-point of BC.

True

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False

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Solution

The correct option is B
False

We have, AB = AC

$\Rightarrow$ A is equidistant from B and C.

$\Rightarrow$ A lies on the perpendicular bisector of BC. (Since the points equidistant from two given points lie on the perpendicular bisector of the line segment joining them).

But, AD is perpendicular to BC. Therefore, D is the mid-point of BC.

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In a ΔABC, it is given that AB = AC and AD is drawn perpendicular to BC. D is not the mid-point of BC.

In a $Δ$ ABC, it is given that AB = AC and AD is drawn perpendicular to BC. D is not the mid-point of BC.