Class 9, Maths, Chapter 10, Exercise 10.5, Solutions
Q.1. In Figure, A,B and C are three points on a circle with centre O such that ∠ BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.
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Q.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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Q. 3. In Figure, ∠ PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠ OPR.
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Q.4. In Figure, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC.
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Q. 5. In Figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠ BAC.
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Q. 6. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC is 30°, find ∠BCD. Further, if AB = BC, find ∠ ECD.
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Q. 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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Q. 8. If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
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Q. 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 Figure). Prove that ∠ ACP = ∠ QCD.
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Q. 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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Q. 11. ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.
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Q.12. Prove that a cyclic parallelogram is a rectangle.
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