A circle is drawn with a line as
diameter and a smaller circle with half the line as
diameter. Prove that any chord of the larger circle
through the point where the circles meet is bisected
by the small circle.
Answers
Answered by
3
AB is the diameter and CD the chord which is equal to the radius and so half of AB. Let the centre be O. If you join C and D to O, and A to C and B to D, you will have three equilateral triangles each side of which is the same as the radius of the circle. The exterior angles CDE and DCE will be 60 degrees, and the third angle of the triangle EDC (which is the same as AEB) = 180 - 60 - 60 = 60 degrees
Similar questions