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6. A,B,C and D are four points on a circle in order such that AB -CD, prove that AC BD00Exemplar] |
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Answer» Draw circle O and mark points A & B on it (I suggest such that central angle AOB is around 30 to 60 degrees. Elsewhere, marks points C & D on the circle with central angle COD equaling angle COD. The arrangement of points on the circle will be such that you go from A to B to C to D by moving clockwise around the circle. Then equal chords AB & CD have equal arcs AB & CD. Note that arc ABC will equal arc BCD, because arc AB + arc BC = arc BC + arc CD. The chords of arc ABC & arc BCD will therefore be equal ("equal arcs have equal chords, on a given circle"). Therefore AC = BD please like the solution 👍 ✔️👍 |
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