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#1 2017-11-04 03:23:42

Animesh
Guest

Radius

Tangents at the points P and Q on a circle meet at R. If PQ = 6 cm and PR = 5 cm find the radius of the circle

#2 2017-11-04 23:05:04

alter ego
Member
Registered: 2012-03-30
Posts: 19

Re: Radius

Hi Animesh,

Join R to the centre, O, of the circle. Triangles OPR and OQR are congruent as they have a 90 degree angle and one side in common plus equal radii, OP and OQ.

So OR is a line of symmetry .  If OR crosses PQ at S then SP = 3,so RS = 4 by Pythagoras.  If you let OS = x and radius = r you can form two equations in r and x by Pythagoras on OPR and on OPS.

It's easier to eliminate r and find x.  Then find r.

Alter

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