Conic Sections: Challenge #3
Geometry
Level
4
Sub-unit: Circles
Let C1 , C2 and C3 be three circles with sides of triangle ABC as their diameter. If the radical axis of the circles C1 , C2 and C3 in pairs meet at point 'R' , then 'R' is :
Circumcentre of triangle ABC
Orthocentre of triangle ABC
Incentre of triangle ABC
Centroid of triangle ABC
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1 solution
Take ABC as right angled triangle. If you draw circles with the sides as diameter, circles will meet at right angled vertex, which is also orthocenter of that triangle.