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

Prove by vertor metord thtat if a line is drawn frome the centre of a circle of a circle to the midpoint of a chord then the line is perpendicular to the chord

In the adjoining figure, seg AB is a diameter of a circle with centre C . Line PQ is a tangent, it touhces the circle at T. segs AP and BQ are perpendiculars to line PQ. Prove seg CP ~= seg CQ .

In the adjoining figure seg RS is the dianeter of the circle with centre 'O' . Point T is in the exterior of the circle . Prove that angleRTS is an acute angle.

A circle with centre 'O' and radius 12cm has chord AB. angleAOB=30^(@). Find A(DeltaAOB).

Construct a circle with centre O and radius 4.3 cm. Draw a chord AB of length 5.6 cm. Construct the tangents to the circle at point A and B without using centre.

In the adjoining figure,seg AB is a diameter of a circle with centre O . Bisector of inscribed angleACB intersects circle at point D. Complete the following proof by filling in the blanks. Prove that : seg AD ~= seg BD

O(0,0) is the centre of a circle whose one chord is AB, where the points A and B are (8,6) and (10,0) respectively. OD is the perpendicular form the centre of the chord AB. Find the coordinates of the midpoint of OD.

Two circle with centre O and P intersect each other in point C and D. Chord AB of the circle with centre O touches the circle with circle with centre P in Point E. Prove that angleADE+angleBCE= 180^(@)

In the given figure, AB and CD are the parallel chords of a circle with centre O. Such that AB = 8 cm and CD = 6 cm. If OMbotAB and OLbotCD distance becween LM is 7 cm. Find the radius of the circle ?

If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.