NCERT Mathematics Class 9 Exemplar Ch 10 Circles Part 5 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Exercise 10.3

Q. 1. If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.

Q. 2. If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc

Q. 3. A, B and C are three points on a circle. Prove that the perpendicular bisectors of AB, BC and CA are concurrent.

Q. 4. AB and AC are two equal chords of a circle. Prove that the bisector of the angle BAC passes through the centre of the circle.

Q. 5. If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.

Q. 6. ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D. Prove that

Q. 7. O is the circumcenter of the triangle ABC and D is the mid-point of the base BC. Prove that .

Q. 8. On a common hypotenuse AB, two right triangles ACB and ADB are situated on opposite sides. Prove that

Q. 9. Two chords AB and AC of a circle subtend angles equal to 90º and 150º, respectively at the centre. Find ∠ BAC, if AB and AC lie on the opposite sides of the centre.

Q. 10. If BM and CN are the perpendiculars drawn on the sides AC and AB of the triangle ABC, prove that the points B, C, M and N are concyclic.

Q. 11. If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides, prove that the quadrilateral so formed is cyclic.

Q. 12. If a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are also equal.

Q. 13. The circumcenter of the triangle ABC is O. Prove that

Q. 14. A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.