I have two questions on which I would greatly appreciate help. I have also included the given solution below.
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:
Thank you very much for your help.