Posts tagged 'sagitta'

F.8 Chord Intersection

If two chords AB and CD of a circle (O, R) intersect at a point X at distance r = |OX| from the center, then the product of their segments is constant and equals the power of X with respect to the circle: |AX|*|BX| = |CX|*|DX| = R^2 - |OX|^2.

F.32 Markowski’s Theorem

If J, K, L denote the perpendicular sagittas from the side midpoints of triangle ABC to the circumcircle, Markowski’s Theorem states J K L = (1/2) r^2 R = (R^2 - d_IO^2)^2 / (8 R).