In the given figure, two circles touch each other at a point ^@C | Math Question and Answer

Answer:

Step by Step Explanation:

We see that $PR$ and $CR$ are the tangents drawn from an external point $R$ on the circle with center $A$ .
Thus, $PR = CR \space \space \space \ldots \text{(i)}$

Also, $QR$ and $CR$ are the tangents drawn from an external point $R$ on the circle with center $B$ .
Thus, $QR = CR \space \space \space \ldots \text{(ii)}$
From $eq \space \text{(i)}$ and $eq \space \text{(ii)}$ , we get
$PR = QR \space \space \text{ [Both are equal to CR]}$

Therefore, $R$ is the midpoint of $PQ$ .
Thus, we can say that the common tangent to the circles at $C$ bisects the common tangent at the points $P$ and $Q$ .

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