In the given figure, two circles touch each other at a point $D$.A common tangent touch both circles at $A$ and $B$ respectively. Show that $CA=CB$.
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Given: In the given figure, two circles touch each other at a point $D$.A common tangent touch both circles at $A$ and $B$ respectively.
To do: To show that $CA=CB$.
Solution:
$\because CA$ and $CD$ are tangents on the points $A$ and $D$ to the circle with centre $O$ from the point $C$.
$\therefore CA=CD\ ......\ ( i)$ [$\because$ tangents drawn to a circle from an external point are equal.]
Similarly, $CB$ and $CD$ are tangents drawn to the circle with centre $O'$ from the point $C$.
Therefore, $CB=CD\ ......\ ( ii)$
From $( i)$ and $( ii)$
$CA=CB=CD$
Thus, it has been proved that $CA=CB$.
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