In two concentric circles with centre O, the radius of the outer ci...

Question

In two concentric circles with centre O, the radius of the outer circle is 25 cm. Chord PQ of the outer circle is tangent to the inner circle at R. If PQ = 14 cm, then the radius of the inner circle is:

Accepted Answer

Since PQ is tangent to inner circle at R, $OR \perp PQ$, and R is the midpoint of PQ, so $PR = 7$ cm. In right triangle $OPR$: $$OR^2 = OP^2 - PR^2 = 25^2-7^2=625-49=576 \Rightarrow OR = 24\ cm$$

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