Hello everyone,

I have two questions on which I would greatly appreciate help. I have also included the given solution below.

Problem:

Question #1:For part (iii), is it possible to solve it using calculus?

By Implicit Differentiation, the circle has "slope": .

The required line has slope and the equation:

The line is tangent to the circle when .

Substitution of the equation of the line at the point of tangency gives:

.

But this does not appear to help too much.

Question #2: This question is based on part (v), but I am trying to find something else that is not asked by the question.Since , the vertex of the triangle is inside the circle.

This means that we are in the case where .

The question does not ask for this, but how would I show that

By basic algebra:

but .

Thank you very much for your help.

Given solution: