Geometry, Plane Geometry, Circles, Tangent to a Circle

A tangent to a circle is a line that touches the circle at exactly one point, the point of tangency. This subject explores properties such as the tangent being perpendicular to the radius at the point of tangency, and lengths of tangents from an external point. Questions involve applying these properties.

• Question

  Consider an arbitrary triangle. Draw tangents to the inscribed circle parallel to the sides of the triangle. These tangents cut off three smaller triangles from the original triangle. Prove that the sum of the radii of the inscribed circles of these smaller triangles is equal to the radius of the inscribed circle of the original triangle.

  Topics:

  Geometry -> Plane Geometry -> Circles -> Tangent to a Circle Geometry -> Plane Geometry -> Triangles -> Triangle Similarity