Page 1 - Home Assignment-6 Cyclic Quadrilateral Ch. 10 circle
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SAI International Residential School
                                                         Class-IX

               Mathematics


               Chapter-10:  Circle


               Home Assignment-6


               Sub topic : Cyclic Quadrilaterals




               1. 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.

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

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

               4. 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 .Prove that
                 ACP =   QCD.








               5. 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.

               6. ABC and ADC are two right triangles with common hypotenuse AC. Prove that  CAD
               =   CBD.

               7. Prove that a cyclic parallelogram is a rectangle.
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