Question

In an isosceles triangle AB = AC and X and Y are midpoints of AB and AC respectively, then the relation between AX and YC is:

• A. $AX=\frac{2}{3}YC$
• B. $AX=2YC$
• C. $AX=\frac{1}{2}YC$
• D. $AX=YC$

Answer 1

The correct option is D $AX=YC$

Given that, x and y are the mid-points of side AB and AC.

$\therefore$
$AX=BX=\frac{1}{2}AB$
$AY=YC=\frac{1}{2}AC$

Given, AB = AC.

We know that,
Euclid's first axiom states that things which are equal to the same thing are equal to one another.

Hence, AX = YC.