CBSE Class 10 Maths Circle

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 - 18

Q1. Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.

Q2. In a quadrilateral ABCD, AB = AC = AD. Show that

Q3. In the figure, O is the centre of the circle and the measure of angle is 1000. find the

Q4. Prove that the angle formed by a chord in the major segment is acute.

Q5. Prove that angle in the semicircle is a right angle.

Q6. BC is a chord of a circle with centre O. A is a point on an arc BC. Prove that

(i) if A is the point on the major arc.

(ii) if A is the point on the minor arc.

Q7. Prove that any cyclic parallelogram is a rectangle.

Q8. Two opposite sides AB and DC of a cyclic quadrilateral ABCD intersect in E, when produced, Prove that triangles EAD and ECB are similar.

Q9. Prove that the quadrilateral formed by angle bisectors of a cyclic quadrilateral is also cyclic.

Please refer to attached file for CBSE Class 10 Maths Circle