Question

the design for a certain stained - glass window calls for a circle inscribed within a triangle, and the triangle then inscribed within a larger circle, as shown in the image below. if the radius of the larger circle is 46.9 centimeters, what is the radius of the smaller circle, rounded to the nearest tenth of a centimeter?
o 16.6
o 18.1
o 19.7
o 21.5
o 23.5
question help: video
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Explanation:

Step1: Recall the property of inscribed and circum - scribed circles of an equilateral triangle

For an equilateral triangle, the radius of the circum - circle ($R$) and the radius of the in - circle ($r$) are related by the formula $R = 2r$.

Step2: Solve for the radius of the in - circle

Given $R=46.9$ cm. Using the formula $r=\frac{R}{2}$. Substitute $R = 46.9$ into the formula: $r=\frac{46.9}{2}=23.45$ cm.

Step3: Round the result

Rounding $23.45$ to the nearest tenth gives $23.5$ cm.

Answer:

E. 23.5