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1. ABCD is a trapezium with AB parallel to DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).
2. You are given a circle. Give a construction to find its center.
3. Prove that the quadrilateral formed by the internal angle bisectors of any
quadrilateral is cyclic.
4. If non-parallel sides of a trapezium are equal, prove that it is cyclic.
1. ABCD is a trapezium with AB parallel to DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).
2. You are given a circle. Give a construction to find its center.
3. Prove that the quadrilateral formed by the internal angle bisectors of any
quadrilateral is cyclic.
4. If non-parallel sides of a trapezium are equal, prove that it is cyclic.
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