Subject: Geometry

Name: Rebecca

Who is asking: Student
Level: Secondary

Question:
How do you prove the following:
Let CD be an altitude of triangle ABC and assume that angle C=90 degrees. Let r1 and r2 be the inradii of triangle CAD and CBD, respectively, and show that r+r1+r2=CD, where r is the inradius of triangle ABC.

Use formulas for area together with the fact that ABC is split by CD into two triangles that are both similar to ABC.

One nice area formula here is rs = ch/2 (where s is the semiperimeter -- s = (a+b+c)/2 -- and h = CD). The similar triangles give you r1/r = b/c and r2/r = a/c.