Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Prove that the two circles which pass through the points 
and touch the straight line 
will cut orthogonaly if 
Text Solution
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Let the equation of the circles be 
….(i)
∵ these circles pass through 
and 
(ii)
And 
….(iii)
solving (ii) and (iii), we get 
put these value of f and d in (i), we get
…..(iv)
equation (v) is quadratic in ' g '
∴ Let 
and 
are its two roots
∵ the two circles represented by (iv) are orthogonal
Hence proved
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