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Question 31
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In the given figure, two identical circles of radius 4 cm touch each other. A and B are the centres of the two circles. If RQ is a tangent to the circle, then what is the length (in cm) of RQ?
Solution
We can say RQ = RS =xÂ
Now PQ =16Â
Also if you consider P to be an external point with respect to circle with center A
Let circles touch each other at M
so we get (PM)(PQ) =PS^2
we get 16(8) =PS^2
so PS =$$8\sqrt{\ 2}$$
Now In triangle PQR
we get $$RQ^2+PQ^2=PR^2$$
We get :
$$x^2+256=\left(x+8\sqrt{\ 2}\right)^2$$
we get $$16\sqrt{\ 2}x\ =128$$
x=$$4\sqrt{\ 2}$$
so RQ =$$4\sqrt{\ 2}$$
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