Question

The radical centre of three circles described on the three sides of a triangle as diameter is

Answer 1

Draw a diagram where Triangle is ABC with circles on it's side having center O on BC, M on AB and N on AC. Let D be the foot of perpendicular on BC.Now,

As MN is parallel to BC, so AD becomes the perpendicular to MN also.

Now as AD is passing through the point of intersection of the circles and also perpendicular to the line joining the centers of the circles, hence it's a radical axis.

Similarly we can prove the other two radical axis.

Now as the lines are both perpendicular and radical axis, their intersection becomes radical center as well as orthocenter.

So, the answer is ORTHOCENTER!!

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