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प्रश्न
If two diameters of a circle intersect each other at right angles, then quadrilateral formed by joining their end points is a
पर्याय
rhombus
rectangle
parallelogram
square
उत्तर
square
The given information in the form of the following figure is as follows:
Since, four sides of the quadrilateral ACBD are four chords which subtend equal angles at the centre. Therefore,
`angleAOC = angleCOB = angleBOD = angleDOA = 90°`
(Since AB and CD are perpendicular diameters)
So sides AC, BC, BD and AD are equal, as equal chords subtend equal angle at the centre.
So , AC = CB = BD = DA …… (1)
We know that diameters subtend an angle of measure 90° on the circle.
So, `angle ACB = angleCBD = angleBDA = angleDAC = 90°` …… (2)
From (1) and (2) we can say that `square AC BD` is a square.
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