Let and . Prove that the ratios of corresponding medians, altitudes, inradii,…

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

Let

\triangle A_1B_1C_1\sim\triangle A_2B_2C_2

and

\frac{A_1B_1}{A_2B_2}=\frac{B_1C_1}{B_2C_2}=\frac{C_1A_1}{C_2A_2}=k

. Prove that the ratios of corresponding medians, altitudes, inradii, exradii, circumradii, and distances between corresponding points, such as

OH

and

GH

, equal

k

. (1) Medians (2) Altitudes (3) Inradii (4) Exradii (5) Circumradii (6) Distance between corresponding points (

OH

GH

, etc.)