Math CentralQuandaries & Queries


Question from edwin, a student:

two perpendicular chords AB and CD intersect at P. if X,Y are their midpoints and M the centre of the circle, prove that MP=XY. i do not a have clue on how to do it so can you please help me with it

Draw a diagram, fairly large and very carefully (use compass for the circle, a ruler for the midpoint, and an accurate right angle to get the chords perpendicular.) What do you notice about the angle AXM? (If you still don't see it try drawing only the circle, the chord AB, its center X, and M.)

You will need to prove that what you observed is really true! Draw triangles AXM and BXM and mark equal sides... what does this tell you about the angles AXM and BXM?

Good Hunting!

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