Chapter 10 – Circles

12. If a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are also equal. 12. If a pair of opposite sides of a cyclic quadrilateral are equal prove that its diagonals are also equal. July 2, 2021 Category: Chapter 10 - Circles , Maths , NCERT Class 9 ,

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. 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. July [...]

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. 10. If BM and CN are the perpendiculars drawn on the sides AC and AB of the triangle ABC C M and N are concyclic. [...]

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

8. On a common hypotenuse AB, two right triangles ACB and ADB are situated on opposite sides. Prove that ∠BAC = ∠BDC. 8. On a common hypotenuse AB two right triangles ACB and ADB are situated on opposite sides. Prove that ∠BAC = ∠BDC. July 2, 2021 Category: Chapter 10 - Circles , Maths , [...]

7. O is the circumcentre of the triangle ABC and D is the mid-point of the base BC. Prove that ∠BOD = ∠A. 7. O is the circumcentre of the triangle ABC and D is the mid-point of the base BC. Prove that ∠BOD = ∠A. July 2, 2021 Category: Chapter 10 - Circles , [...]

6. ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D. Prove that ∠CBD + ∠CDB = 1/2 ∠BAD 6. ABCD is such a quadrilateral that A is the centre of the circle passing through B C and D. Prove that ∠CBD + ∠CDB = 1/2 [...]

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. 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. July [...]

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. 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. July 2, 2021 [...]

3. A, B and C are three points on a circle. Prove that the perpendicular bisectors of AB, BC and CA are concurrent. 3. A B and C are three points on a circle. Prove that the perpendicular bisectors of AB BC and CA are concurrent. July 2, 2021 Category: Chapter 10 - Circles , [...]