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The sum of the two opposite angles of a quadrilateral inscribed in a circle is two right angles.
If two angles of a quadrilateral are supplementary, the four vertices are concyclic.
Prove that the angle inscribed in a semi circle is a right angle.
A chord AB one of the two concentric circles intersects the other circle at points C and D . Prove that , AC= BD.
A circle passes through the vertices of a right angled triangle. Show that the centre of the circle is the middle point of the hypotenuse.
Two chords AB and AC of a circle subtend equal angles with the radius passing through A. Prove that AB = AC.
Prove that the straight line joining the middle points of two parallel chords of a circle passes through the center and is perpendicular to the chords