An isosceles triangle is situated in a circle such that its base is a chord of length 10 cm, its height is 10 cm, and its vertex angle is at the center of the circle.

Question

An isosceles triangle is situated in a circle such that its base is a chord of length 10 cm, its height is 10 cm, and its vertex angle is at the center of the circle. What is the diameter of the circle?

Answer 1

This might be a tough question to answer without being able to include a picture, so I will assume you can draw the picture accurately. Since the base of the triangle is a chord that is 10 cm long, the height of the triangle intersects the base at the midpoint of the chord, dividing it into two 5 cm segments. You can then draw a radius to the endpoints of the chord which will create right triangles.

The legs of the right triangle are 5 cm (half the chord) and 10 cm (the height of the triangle). This means we can use the Pythagorean Theorem to find the hypotenuse of the right triangle (the radius of the circle).

5² + 10² = r²

25 + 100 = r²

125 = r²

√125 = r

√25•5 =r

5√5 = r

To get the diameter, double the radius. The diameter is 10√5

Hope this helps.

:)