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ICSE Class 9 Answered

In the given figure, equal chords AB and CD of a circle with centre O cut at right angles at P. If L and M are midpoints of AB and CD respectively, prove that OLPM is a square.
Asked by pereiracalida | 14 Jan, 2018, 06:38: PM
answered-by-expert Expert Answer
begin mathsize 16px style SInce space straight L space and space straight M space are space the space midpoints space of space AB space and space CD space respectively comma
rightwards double arrow angle OLB equals angle OMD equals 90 degree
rightwards double arrow angle OLP equals angle OMP equals 90 degree
SInce space equal space chords space of space straight a space circle space are space equidistant space from space the space centre comma
OL equals OM
In space triangles space OLP space and space OMP comma
OL equals OM
angle OLP equals angle OMP
OP equals OP
rightwards double arrow triangle OLP approximately equal to triangle OMP
rightwards double arrow LP equals MP
Thus comma space in space quadrilateral space OLPM comma
OL equals OM comma space LP equals MP space and space angle OLP equals angle OMP equals 90 degree
Hence comma space OLPM space is space straight a space square. end style
 
Answered by Rashmi Khot | 15 Jan, 2018, 10:13: AM

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