Question

In figure, $KXM$ is a tangent to the circumcircle $C$ of $△XYZ$ such that $LM\parallel YZ$. Show that $XY=XZ$

Answer 1

Since $Lm||yz$

So, $\angle LXY=\angle XYZ$ (alternate angles)

and $\angle MXZ=\angle XZY$ (alternate angles)

Now,

Since Angle between tangent and chord is equal to angle made by chord in the alternate segment.

So, $\angle LXY=\angle XZY$

and So, $\angle XYZ=\angle XZY$

hence,

$XY=XZ$ [$\because$ Sides opposite to the equal angles are also equal.]