Define a chord of a circle. What is the longest chord of a circle called?

State the theorem concerning the line segment drawn from the centre of a circle to the midpoint of a chord.

State the converse of the theorem in question 2.

A chord AB of a circle with centre O has a length of 8 cm. The midpoint of AB is C. If the radius of the circle is 5 cm, find the length of OC.

A perpendicular is drawn from the centre O of a circle to a chord PQ, meeting it at R. If the radius is 10 cm and OR = 8 cm, find the length of the chord PQ.

PQ and RS are two parallel chords of a circle, on opposite sides of the centre O. The radius is 10 cm, PQ = 16 cm, and RS = 12 cm. Find the distance between the two chords.

AB and CD are two equal chords of a circle with centre O. The midpoints of the chords are X and Y. Prove that OX = OY.

In a circle with centre O, R is the midpoint of chord PQ. If OP^R=30∘, prove that △ORQ is a right-angled isosceles triangle.

AB and BC are two equal chords of a circle with centre O. Perpendiculars from O meet the chords at X and Y respectively. If XO^Y=140∘, find the magnitude of AB^C.

The vertices A, B, and C of △ABC lie on a circle with centre O. The midpoint of BC is X. If O lies on AX, what type of triangle is ABC? Prove your answer.

PQ and RS are two equal chords of a circle with centre O. The midpoints of PQ and RS are X and Y respectively. Prove that XO^Y=PS^R.

A chord of length 24 cm is 5 cm away from the centre of a circle. Another chord is 12 cm away from the centre. Find its length.

The perpendicular from the centre O of a circle to a chord AB intersects the chord at X and meets the circle at Y. If XY = 3 cm and AB = 8 cm, find the radius of the circle.

The vertices A, B, and C of an equilateral triangle lie on a circle with centre O. Perpendiculars are drawn from O to AB, AC, and BC, meeting them at X, Y, and Z respectively. Prove that OX = OY = OZ.

PQ and PR are two chords of a circle with centre O. Perpendiculars from O meet PQ and PR at X and OY respectively. If XR and QY are straight lines, prove that PQ=PR.