Three equal circles of radius R touch each other externally. Find the sides and angle
| May 7, 2021 | education
Three equal circles of radius R touch each other externally. Find the sides and angle of the triangle whose vertices are the tangent points.
Let the points M, H and K be the points of tangency of the circles.
Connect the centers of circles A, B and C.
The formed triangle ABC is equilateral, since AB = BC = AC = 2 * R see.
Segments AM = AK = BM = ВН = СK = CH = R see.
Then the segments KM, KН and MН are the middle lines of the triangle ABC, then KM = KН = MН = AB / 2 = 2 * R = R, and therefore the KMН triangle is equilateral.
An equilateral triangle has all internal angles of 60.
Answer: The sides of the triangle are equal to R cm, the angles of the triangle are 60.
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