Point of tangency of an inscribed circle divides a leg of an isosceles triangle into 3 cm and 4 cm line segments (considered from the vertex to the base). Find the perimeter of the triangle.

Answer 1

You can think of the sides of the triangle as tangent lines to the circle from the vertices of the triangle and remember that the line segments of the tangents from a point to the circle are of equal length.

The point of tangency on the other leg will divide the leg in the same way, 3 and 4. If the shorter part of the leg is touching the base, the base will have a length of (3+3 =6), otherwise it will have a length of (4+4 =8)

Therefore the triangles perimeter is either 7+7+6=20 0r 7+7+8=22