ABC is a triangle, circle C1, C2, C3 are drawn with sides AB, BC, CA as their diameters. The radical axis between any 2 circles w.r.t. triangle abc is one of its altitude. how?

We know that if two circles are drawn by taking the sides of triangle as diameterthen they will intersect at third side.

Now angle ADC and amgle ADB are the angle in semicircle so they will be 90 degree each and hence AD is the altitude itself.Similarly you can prove by taking other sides as dimater too.

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