Question

If the chords of a circle are 12cm and 6cm and the distance between them is 3cm. Find the radius of the circle

Answer 1

Answer on Question#39892 – Math - Geometry

Question.

If the chords of a circle are $12\mathrm{cm}$ and $6\mathrm{cm}$ and the distance between them is $3\mathrm{cm}$ . Find the radius of the circle.

We have: $AC = 12/2 = 6$ , $BD = 6/2 = 3$ , $CD = 3$ , $OA = OB = r$ .

Solution.

Let $OC = x$ , then $OD = x + CD = x + 3$ .

From right triangle OAC: $OA^2 = AC^2 + OC^2 \rightarrow r^2 = 36 + x^2$ .

From right triangle OBD: $OB^2 = BD^2 + OD^2 \rightarrow r^2 = 9 + (x + 3)^2$ .

So, $36 + x^{2} = 9 + (x + 3)^{2}\rightarrow 36 + x^{2} = 9 + x^{2} + 6x + 9\rightarrow x = 3,$

$r^2 = 36 + x^2 = 36 + 9 = 45 \rightarrow r = \sqrt{45} = 3\sqrt{5}$ .

Answer: $r = \sqrt{45} = 3\sqrt{5} \, \text{cm} \approx 6.71 \, \text{cm}$.