Question

An isosceles triangle with each leg measuring 13 is inscribed in a circle. If the altitude to the base of the triangle is 5, find the radius of the circle.

Answer 1

Answer:

Correct answer: R = 16.9 units

Step-by-step explanation:

The center of the circle described around the obtuse triangle lies outside the inner area of the triangle and is obtained in the cross section of the sides. Here we have two similar triangles whose corresponding sides are proportional and the radius of the circle is  R = 5 + x

13 : 5 = (5 + x) : 13/2  ⇒ 5 · (5 + x) = 13²/2  ⇒ 5 x + 25 = 169/2

5 x = 169/2 - 25 = (169 - 50)/2 = 119/2  ⇒ x = 119/10 = 11.9

R = 11.9 + 5 = 16.9 units

R = 16.9 units

Sorry, but I don't have the tools to draw a proper drawing.

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