In a circle with centre 'O' . `bar(AB)` is a chord and 'M' is its midpoint . Now prove that `bar(OM)` is perpendicular to AB

In the adjacent figure, AB is a chord of circle with centre O. CD is the diameter perpendicualr to AB. Show that AD = BD

Two chords AB and CD of a circle with centre O intersect each other at the point P. prove that AOD+ angle BOC = 2 angle PBC . If angle BOC are supplementary to each other, then prove that the two chords are perpendicular to each other.

If two chords AB and CD of a circle with centre, O, when producd intersect each other at the point P, prove that angle AOC- angle BOD=2 angle BPC .

In the figure, O is the centre of the circle and AB = CD. OM is perpendicular on bar(AB) and bar(ON) is perpendicular on bar(CD) . Then prove that OM = ON.

AB and CD are two chords of a circle with centre at O , the ratio of lengths of which is 4: 5. If the perpendicular distance of AB from O be d cm, then perpendicular distance of CD from O.

AB is a diameter of a circle with centre O and AC is a chord . The straight line through O parallel to AC meets the arc BC at D. Prove that, BD= CD.

Two chords AB and CD of the circle with centre at O intersect each other at an internal point P of the centre. Prove that angle AOD+ angle BOC=2 angle BPC

AC is a diamter of a circle with centre O, If triangleABC is cyclic and OP bot AB , then prove that OP:BC = 1:2.

O is the centre of a centre having diameter AB. P is any point on the circle. Draw a perpendicular from P to AB, which meets AB at N. Prove that PB^2 =AB.BN

If two chords AB and CD of a circle with centre O, when produce intersect each other at the point P, then prove angleAOC-angleBOD = 2angleBPC .