#### 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)`

Is there an error in this question or solution?

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.