The Book of Lemmas Proposition 11 - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim

The Book of Lemmas: Proposition 11

Main Concept

If two chords in a circle, AB and CD, intersect at right angles in a point O, not being the center, then:

AO2 + BO2 + CO2 + DO2 = diameter2.


Click on the plot to create points A and B on the circle's perimeter. Adjust the slider to move the x-coordinate, xO , of the point O, where the two lines intersect. Note that the sum of the squares of distances between points A, B, C and D is equal to the square of the diameter of the circle.



Arc Lengths:

AO2            =      

BO2            =      

CO2            =      

DO2            =      



diameter2      =      


r AO2 + BO2 + CO2 + DO2 = diameter2


     xO  CD                  


More MathApps