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Two circles of equal radii cut each othe...

Two circles of equal radii cut each other at P and Q, so that the centre of one lies on the other. A straight line through P cuts the circle again at A and B. Prove that `Delta`QAB is equilateral triangle.

Text Solution

Verified by Experts

`QC^2=r^2-(r/2)^2`
=`3/4r^2`
`QC=sqrt3/2r`
`/_QOP=2*/_QOC`
=`120^0`
`/_QRP=120/2=60^0`
`/_QRP and /_QBP` are inscribed on the arc PQ,
`theta=60^0`
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