The diagram below (not drawn to scale) shows the diagram of a medal plaque. The plaque consists of a circle with center O, a uniform circular ring with center B and triangle OFG. OD is the height of the triangle OFG. AOE = 16 cm, BC = 2 cm, DF = DG = 6.61 cm and DE = 3.5 cm.

(a)
Show that OD is 4.5 cm.
(b)
The shaded region will be painted with gold paint which cost $2.00 per cm^2. The un-shaded region will be painted with silver paint which cost $1.20 per cm^2.

Find the cost of painting of the plaque.

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Worked solution

1. Find $OD$ from the radius of the outer circle and the given length $DE$.

Since $AOE = 16\text{ cm}$ is the diameter of the outer circle,

$OE = \frac{16}{2} = 8\text{ cm}.$

Also, $O$ , $D$ and $E$ are collinear, so

$OD = OE - DE = 8 - 3.5 = 4.5\text{ cm}.$

Answer

Hence, $OD = 4.5\text{ cm}$ .

AI analysis — may contain mistakes.

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