NCERT Solutions for Class 9 Maths Chapter 10 Circles — Exercise 10.5

NCERT class 9 maths chapter 10 Circles

Question 1:In Fig. 10.36, A,B and C are three points on a circle with centre O such that Ð BOC = 30° and Ð AOB = 60°. If D is a point on the circle other than the arc ABC, find ÐADC.

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Question 2:A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

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Question 3:In Fig. 10.37, Ð PQR = 100°, where P, Q and R are points on a circle with centre O. Find Ð OPR.

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Question 4:In Fig. 10.38, Ð ABC = 69°, Ð ACB = 31°, find Ð BDC.

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Question 5:In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that Ð BEC = 130° and Ð ECD = 20°. Find Ð BAC.

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Question 6:ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If Ð DBC = 70°, Ð BAC is 30°, find Ð BCD. Further, if AB = BC, find Ð ECD.

Question 7:If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

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Question 8:If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

EXERCISE 10.51. In Fig. 10.36, A,B and C are three

Question 9:Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. 10.40). Prove that Ð ACP = Ð QCD.

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Question 10:If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

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Question 11:ABC and ADC are two right triangles with common hypotenuse AC. Prove that Ð CAD = Ð CBD.

Question 12:Prove that a cyclic parallelogram is a rectangle.