oabc is a rhombus whose 3 vertices a b and c lie on the circle with centre o if - Maths - Circles

Question

oabc is a rhombus whose 3 vertices a b and c lie on the circle
with centre o if thre radius of the circle is 10 cm , find the area
of the rhombus

Chetna Khanna · Accepted Answer

Given: OABC is a rhombus whose three vertices A, B, C lies on circle with centre O and radius 10 cm

O is the centre of circle, OABC is a Rhombus Suppose the diagonals of the Rhombus OABC intersects at S Radius of circle, r = 10 cm âˆ´ OA = OB = OC = 10 cm We know that diagonals of rhombus Bisect each other at 90Â° $∴ OS = SB = \frac{10}{2} = 5 cm and SC = SA$ In rt âˆ†OCS, OC2 = OS2 + SC2 â‡’ (10)2 = 52 + SC2 â‡’ SC2 = 100 â€“ 25 â‡’ SC2 = 75 $\Rightarrow SC = 5 \sqrt{3} cm ∴ AC = 2 × SC = 2 \times 5 \sqrt{3} = 10 \sqrt{3} cm$ We know that, $Area of Rohmbus = \frac{1}{2} \times length of one diagonal × Length of other diagonal = \frac{1}{2} \times 10 \times 10 \sqrt{3} = 50 \sqrt{3} {cm}^{2}$

oabc is a rhombus whose 3 vertices a.b and c lie on the circle with centre o. if thre radius of the circle is 10 cm , find the area of the rhombus