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प्रश्न
In a circle with centre O, AB and CD are two diameters perpendicular to each other. The length of chord AC is
विकल्प
2AB
- \[\sqrt{2}\]
- \[\frac{1}{2}AB\]
- \[\frac{1}{\sqrt{2}}AB\]
उत्तर
We are given a circle with centre at O and two perpendicular diameters AB and CD.
We need to find the length of AC.
We have the following corresponding figure:
Since, AB = CD (Diameter of the same circle)
Also, ∠AOC = 90°
And, AO = `(AB)/2`
Here, AO = OC (radius)
In ΔAOC
`AC^2 = AO^2 + OC^2 = AO^2 + AO^2`
`= ((AB)/2)^2 + ((AB)/2)^2`
`AC^2 = (AB^2)/2`
`AC = (AB)/(sqrt(2))`
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