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Question
OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. If the radius of the circle is 10 cm, find the area of the rhombus.
Solution
Radius = 10 cm
In rhombus OABC,
OC = 10 cm
∴ `OE = 1/2 xx OB`
= `1/2 xx 10`
= 5 cm
In right ΔOCE,
OC2 = OE2 + EC2
`=>` 102 = 52 + EC2
`=>` EC2 = 100 – 25 = 75
`=>` EC = `5sqrt(3)`
∴ AC = 2 × EC
= `2 xx 5sqrt(3)`
= `10sqrt(3)`
Area of rhombus = `1/2 xx OB xx AC`
= `1/2 xx 10 xx 10sqrt(3)`
= `50 sqrt(3) cm^2 ≈ 86.6 cm^2` ...`(sqrt(3) = 1.73)`
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