NCERT Solutions for Class 9 Maths Exercise 10.6 Circles

Exercise 10.6 the extension of theorem 10.8 gives rise to another theorem 10.9 which says that angles are in the same segment of the circle are equal. Now, this very easy to prove.

Theorem 10 says that if a line segment joining 2 points of a circle subtends equal angles at two other point lying on the same side of the line containing the line segments. The four points are con-cyclic that is the four points lie on the same circle.

You will not find theorems and questions difficult, if you practice questions relating the correct theorem. Theorem 10.11 says that in case of cyclic quadrilateral the sum of either pair of opposite angles is 180 degree.

The theorem 10.12 is the converse of theorem 10.11 and it says that sum of the pair of opposite angles of a quadrilateral is 180. The quadrilateral must be cyclic.

Exercise 10.6 contains 8 questions out of which number 1, 4, 5, 6, 7, and 8 are questions requiring proof of certain statement.

Whereas, question number 2 and 3 require finding out the length of either the radius of the segment of a circle. After practicing once or twice, questions given in exercise looks easier to solve.

Before attempting this exercise it advised to go through all theorems in this chapter from theorem 1 to 12. Particularly, the following two important ones.

Angle subtended by an arc in the centre is double the angle subtended by it at any point on the remaining part of the circle (theorem 8). The sum of either pair of opposite angles of a cyclic quadrilateral is 180 (theorem 11).