Question

ABC is an equilateral triangle inscribed in a circle with centre 0. Radius OB = 4 cm, and OM is perpendicular to BC. Find x and the perimeter of the triangle.

Answer 1

Given:

△ABC is equilateral, inscribed in a circle 

Radius OB = 4 cm

OM ⊥ BC

Find x = BM, = BM, and the perimeter of triangle ABC.

Step 1: Use the triangle ΔOMB

In an equilateral triangle, Centre O is also the centroid.

In right triangle △OMB:

hypotenuse OB = 4

∠MOB = 30°

`sin(30°) = x/4`

= `1/2 = x/4`

= x = `2sqrt3`   

Step 2:

Since x = BM = `2sqrt3`, and M is midpoint of BC,

BC = 2x = `4sqrt3`

Perimeter = `3 xx 4sqrt3`

Perimeter = `12sqrt3` cm