Chapter 9 : Circle

• Circle is a closed figure of points which are at a constant distance from a fixed points, centre and constant distance is called radius.
• Two circles are congruent if and only if they have equal radii.
• Equal chords of a circle subtend equal angles at the centre and conversely.
• Two arcs of a circle are congruent if their corresponding chords are equal and conversely.
• The perpendicular drawn from the centre of a circle to a chord bisects the chord.
• The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

Exercise - 17

Q. 1. If two circles intersect each other at two points, prove that the line joining their centres is the perpendicular bisector of their common chord.

Q. 2. Two chords AB and AC of a circle are equal. Prove that the bisector of LBAC passes through the centre of the circle.

Q. 3. In the adjoining figure, l inter intersects two concentric circles with common centre O at A, B, C and D. prove that AB = CD.

Q. 4. In the adjoining figure, O is the centre of the circle of radius 5cm. AB = 6cm, CD = 8cm. Determine PQ

Q. 5. In the adjoining figure, of a circle with centre O. If BC is a diameter, prove that CA = 20D.

Answers