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Oabc is a Rhombus Whose Three Vertices A, B and C Lie on a Circle with Centre O. (I) If the Radius of the Circle is 10 Cm, Find the Area of the Rhombus - ICSE Class 10 - Mathematics

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Question

OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O.
(i) If the radius of the circle is 10 cm, find the area of the rhombus

Solution

i) Radius = 10 cm
In rhombus OABC,
OC = 10 cm
∴ `OE= 1/2 ×  OB =1/2 × 10 = 5 cm`
In Rt. ΔOCE,
 `OC^2  =  OE^2  + EC^2`
`⇒ 10^2 =  5^2 +  EC^2`
`⇒ EC^2 = 100 - 25 =75`
`⇒ EC =  5sqrt( 3)`

∴ AC =` 2 xx EC = 2 xx 5sqrt( 3) = 10 sqrt(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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Solution Oabc is a Rhombus Whose Three Vertices A, B and C Lie on a Circle with Centre O. (I) If the Radius of the Circle is 10 Cm, Find the Area of the Rhombus Concept: Chord Properties - Equal Chords Are Equidistant from the Center.
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