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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. Question 9 Question 11 Prerequisite It is bit tricky question to solve…
Read MoreQuestion 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 ∠ACP = ∠QCD.…
Read MoreQuestion 8: If the non-parallel sides of a trapezium are equal, prove that it is cyclic. Question 7 Question 9 Prerequisite Primarily, this entire chapter is based on the cyclic quadrilateral and its properties. To prove that the given trapezium…
Read MoreQuestion 7: If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle. Question 6 Question 8 Prerequisite This question has been solved by two different methods –…
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Question 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. Question 5 Question 7 Prerequisite Most…
Read MoreQuestion 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 ∠ BEC = 130°and ∠ ECD = 20°. Find ∠ BAC. Question 4 Question…
Read MoreQuestion 4: In Fig. 10.38, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC. Question 3 Question 5 Prerequisite Simple! Concepts used: Angle sum property of triangle Angles in the same segment of a circle are equal Theorem…
Read MoreQuestion 3: In Fig. 10.37, ∠ PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠ OPR. Question 2 Question 4 Prerequisite Questions are always easy to solve. All you need to…
Read MoreQuestion 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. Question 1…
Read MoreQuestion 1: In Fig. 10.36, 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…
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