In triangle ABC AA1, BB1 and CC1 are medians. The ratio АA1: BC = 3: 2. Find the angle between

In triangle ABC AA1, BB1 and CC1 are medians. The ratio АA1: BC = 3: 2. Find the angle between BB1 and CC1.A) 45 ° B) 60 ° C) 90 ° d) 120 °

Let m. O be the point of intersection of the medians.

1. The ratio of the sides is known: АА1: ВС = 3: 2;

2. BA1 = A1C, since A1 is the middle of the BC;

3. point O divides the median AA1 in a ratio of 2: 1, counting from the top.

From these three sentences it follows that OA1 = BA1 = A1C.

A circle can be drawn through points B, O, C (a circle can be drawn through any 3 points). Since A1O = A1B = A1C, A1 is the center of this circle, BC is the diameter. Angle BOC = 90 ‘, it is inscribed and rests on a semicircle.

The angle between BB1 and CC1 is the angle B1OC (acute angle), 180 ‘- BOC = 180’ – 90 ‘= 90’.

Answer: the angle between BB1 and CC1 is 90 ‘, point c).