Perpendicular bisectors of two chords of a circle intersect at centre.

Theorem :-2The perpendicular from centre of a circle to the chord bisects the chord and Perpendicular bisectors of two chords of a circle intersects at the centre.

If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA cong"arc "PYB .

Consider the following statements I. The perpendicular bisector of a chord of a circle does not pass through the centre of the circle. II. The angle in a semicircle is a right angle. Which of the statements given above is/are correct?

Consider the following statements : 1.The perpendicular bisector of chord of a circle does not pass through the centre of the circle. 2. The angle in a semicircle is a right angle. Which of the statements given above is/are correct ?

Prove that the perpendicular bisector of a chord of a circle always passes through the centre.

Theorem of internal division of chords. Suppose two chords of a circle intersect each other in the interior of the circle, then the product of the lengths of the two segments of one chord is equal to the product of the lengths of the two segments of the other chord. Given : (1) A circle with centre O . (2) chords PR and QS intersect at point E inside the circle. To prove : PE xx ER = QE xx ES Construction : Draw seg PQ and seg RS

Prove that the right bisector of a chord of a circle,bisects the corresponding arc or the circle.

Prove that the right bisector of a chord of a circle,bisects the corresponding arc or the circle.

In any triangle ABC,if the angle bisector of /_A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the triangle ABC