The given figure shows a circle with centre O. P is mid-point of chord AB. Show that OP is perpendicular to AB.

The given figure shows a triangle ABC, in which AB gt AC. E is the mid-point of BC and AD is perpendicular to BC. Prove that : AB^(2) +AC^(2) =2BE^2 +2AE^2

The given figure shows a triangle ABC, in which AB gt AC . E is the mid-point of BC and AD is perpendicular to BC. Prove that AB^(2)- AC^(2)= 2BCxxED .

The following figure shows a circle with centre O. If OP is perpendicular to AB, prove that AP = BP.

The given figure shows a circle with centre O and BCD is tangent to it at C. Show that /_ACD+/_BAC=90^(@)

In the given figure, AB and CD are two equal chords of a circle, with centre O. If P is the mid-point of chord AB, Q is the mid-point of chord CD and anglePOQ = 150^(@) find angleAPQ

(Converse of Theorem 3) The line joining the centre of a circle to the mid-point of a chord is perpendicular to the chord.

In the figure given below, O is the centre of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD. AB = 24 cm, OM = 5 cm, ON = 12 cm. Find the : (i) radius of the circle (ii) length of chord CD

In the given figure, AB is diameter of the circle with centre O. AQ, BP and PRQ are tangents. Prove that OP and OQ are perpendicular to each other.

In the given figure, the diameter CD of a circle with centre 0 is perpendicular to the chord AB. If AB = 8 cm and CM = 2 cm, find the radius of the circle.

Draw a circle with centre at a point O and radius 5.6 cm. Draw any chord AB. Draw a perpendicular bisector of AB. Does the bisector pass through the centre O ?