Question

ABC is an equilateral triangle of side 6 cm. If a circle of radius 1 cm is moving inside and along the side of the triangle, then locus of centre of circle is an equilateral triangle of side is:

Answer 1

Answer:

The answer of this question is 2x1.732=3.464cm

Answer 2

The locus of centre of circle is an equilateral triangle of side is 6 - 2√3

The circle must be centered on the angle bisector, and from either side of the original triangle must be 1 cm.

Slope of the median = Tan 30 = 1√3

Tan 30 = 1/x

1/√3 = 1/x

x = √3

The inner triangle's bottom edge ends at (6, 0) a close x-distance from the apex.

The center of the larger triangle is about √3 from one edge, and the edge length is about 2√3 times that distance. The distance from the centroid to the edge of the smaller triangle will be about √3-1, and this distance will be about 6-2√3 times this distance.

Therefore,

Side of small Δ = 6 - 2x = 6 - 2√3