Let P & Q be the extremities to the left and right of B. /_PAB=90 and also /_PDQ=90. AB//DQ or AB//CD. Similarly, BC//AD and thus ABCD is a rectangle whose diagonals AC & BD are equal while M bisects both. Ajit
Straightness of PAD and DCQ can be proven by observing the following rule in 3 circles: "An inscribed angle subtended by a diameter is a right angle". Rest should be easy.
Let P & Q be the extremities to the left and right of B. /_PAB=90 and also /_PDQ=90. AB//DQ or AB//CD. Similarly, BC//AD and thus ABCD is a rectangle whose diagonals AC & BD are equal while M bisects both.
ReplyDeleteAjit
But this assumes that PAD and DCQ are straight. How do we know this?
ReplyDeleteYes it does.
ReplyDeleteStraightness of PAD and DCQ can be proven by observing the following rule in 3 circles:
"An inscribed angle subtended by a diameter is a right angle". Rest should be easy.