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Rhombus

OABC is a rho...

Question

OABC is a rhombus. Find $m ∠ A O C$

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Solution

OA = AB = BC = OC ...(1)
[OABC is a rhombus]

OA = OB = OC ...(2)
[Radii of the circle]

$Δ B A O$ is an equilateral triangle
[Steps 1 and 2]

$m ∠ A O B = m ∠ C O B = 60^{\circ}$
[Angles of equilateral triangles]

$m ∠ A O C = m ∠ A O B + m ∠ C O B = 120^{\circ}$

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