The median bm of triangle ABC is the diameter of the circle intersecting side BC at its midpoint.

The median bm of triangle ABC is the diameter of the circle intersecting side BC at its midpoint. The side length is 4. Find the radius of the circumscribed circle of triangle ABC.

Point N divides BC in half: BN = NC.

VM is the diameter of the small circle. <BNM is based on the diameter of the BM, therefore, it is straight.

Triangles BNM and MNC are equal, because they are rectangular, have a common leg NM, and their legs BN and NC are equal. From the equality of the triangles it follows: BM = MC.

VM is the median, therefore AM = MC. From the last two equalities it follows that BM = AM = MS.

We have three points – A, B, C, – which are equally distant from point M. This is possible if point M is the center of the great circle, and the segments BM, AM, MS are its radii. AC is the chord passing through the center of the circle, therefore AC is the diameter of the circle. The radius is half the diameter: r = AC / 2 = 4/2 = 2.

Answer: 2.