If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord.
Prove that among all the chords of a circle passing through a given point inside the circle that one is smallest which is perpendicular to the diameter passing through the point.
Two circles with centres O and O′ intersect at two points A and B. A line PQ is drawn parallel to OO′ through A(or B) intersecting the circles at P and Q. Prove that PQ = 2 OO′.
A quadrilateral ABCD is inscribed in a circle such that AB is a diameter and ∠ADC = 130º. Find ∠BAC.
A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment
If a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are also equal.
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