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CBSE Class 9 Answered

prove that the circle drawn with any side of a rhombus as diameter passes through the point of intersection of its diagonals
Asked by jhmukherjee94 | 08 Mar, 2016, 10:35: PM
answered-by-expert Expert Answer
begin mathsize 16px style Let space PQRS space be space straight a space rhombus space with space diagonals space PR space and space QS space which space intersect space at space straight O. space space We space know space that space diagonals space of space rhombus space intersect space each space other space at space right space angles. space rightwards double arrow angle POQ equals angle QOR equals angle ROS equals angle SOP equals 90 degree Here space we space have space circles space passing space through space PQ comma space QR comma space RS comma space SP space as space diameter and space they space pass space through space straight O. space For space the space circle space with space PQ space as space diameter comma space we space have space angle POQ space inscribed space in space the space semi minus circle. space Also space angle space inscribed space in space straight a space semi minus circle space is space straight a space right space angle. space space Thus comma space the space circle space passes space through space straight O. space space This space is space true space for space any space circle space constructed space on space any space of space the space side space of space rhombus. space Therefore comma space circle space with space the space side space of space rhombus space as space diameter space passes space through space the space point space of space intersection space of space its space diagonals. end style
Answered by Rashmi Khot | 09 Mar, 2016, 12:00: PM

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