The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm. find the length of a diameter of the circle circumscribed about this triangle.

ANSWER

The length of a Diameter is 3.714

EXPLANATION

The circumscribed triangle is shown in the attachment.

We use the cosine ratio to find the altitude of the isosceles triangle.

Altitude =8cos(60°)

Altitude=4cm

Let the upper half of the altitude be y cm.

Then the radius of the circle is (y-4)cm

The upper radius meets the tangent at right angles.

From the smaller right triangle,

y=1.857

The diameter is 2y

=2(1.875)

The length of a Diameter is 3.714