1. The distance between centers of two circles of radii 3 cm and 8 cm is 13 cm. If the points of contact of a direct common tangent to the circles are P and Q, the length of the line segment PQ is:
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- By: anil on 05 May 2019 02.19 amTwo circles having radii $$r_1$$ and $$r_2$$ and distance between them $$d$$ Length of direct common tangent PQ = $$sqrt{d^2-(r_2-r_1)^2}$$ = $$sqrt{(13)^2-(8-3)^2}$$ = $$sqrt{169-25}=sqrt{144}=12$$ cm => Ans - (C)
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In the adjoining figure I and II are circles with centres P and Q respectively, The two circles touch each other and have common tangent that touches them at points R and S respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in the ratio 4: 3. It is also known that the length of PO is 28 cm.What is the ratio of the length of PQ to that of QO?[CAT 2004]