Let and be the lengths of the sides of a nondegenerate triangle, let , and let and be the inradius and circumradius of the triangle, respectively. Show that

and determine the cases of equality.

**My solution.**

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# Category: College Math

## Solution of problem 11306 in AMM

## Problems in Section 2 of GTM 167

## Problems in Section 1 of GTM 167

Lecture Notes in Mathematics, High School Olympiads

Let and be the lengths of the sides of a nondegenerate triangle, let , and let and be the inradius and circumradius of the triangle, respectively. Show that

and determine the cases of equality.

**My solution.**

Please post carefully solutions of following problems:

1. Show that the only automorphism of is the identity.

Please post carefully solutions of the following ones:

1. Let be a field extension of . By defining scalar multiplication for and by , the multiplication in , show that is an vector space.

2. If is a field extention of , prove that iff .