The figure below shows a circle with center O and radius 6 cm. A, B, C, D belong to the circle, such that lines AB and CD are perpendicular. Point M is the midpoint of chord AB and OM=3 cm.[br]1. Find OM.[br]2. Calculate[math]AC^2+BD^2[/math]
Construct point E, diametrically opposite to C.[br]Then the angle EAC=EDC =...............
[img]data:image/png;base64,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[/img]
[math]AC^2+BD^2=......[/math]
Pythagorean Theorem in triangle EAC. [br]144