In the given figure, ^@ XP ^@ and ^@ XQ ^@ are the two tangents | Math Question and Answer

Answer:

Step by Step Explanation:

We know that the lengths of tangents drawn from an external point to a circle are equal.

Thus $\begin{aligned} & XP = XQ && \text{[Tangents from X]} && \ldots \text{(i)} \\ & AP = AR && \text{[Tangents from A]} && \ldots \text{(ii)} \\ & BR = BQ && \text{[Tangents from B]} && \ldots \text{(iii)} \end{aligned}$
We also see that $XP = XA + AP$ and $XQ = XB + BQ$ .

Thus, $\begin{aligned} & XP = XQ && \text{[Using (i)]} \\ \implies & XA + AP = XB + BQ \\ \implies & XA + AR = XB + BR && \text{[Using } eq \text{ (ii) and } eq \text{ (iii)]} \end{aligned}$
Thus, $XA + AR = XB + BR$ .

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