Problem #DES-010225
Problem
Certain geometric objects nicely blend when they happen to be
together in a problem. One possible example of such a pair of objects is
a circle and an inscribed angle.
We will be using the following statements in the examples and
problems:
1. The supplementary angles (angles “hugging" a straight line) add up to
\(180^{\circ}\).
2. The sum of all internal angles of a triangle is also \(180^{\circ}\).
3. Two triangles are said to be “congruent" if ALL of their
corresponding sides and angles are equal.
The following terminology will also be quite helpful. In the picture
below, the points \(B\) and \(C\) lie on the circumference of the circle
while the vertex \(A\) lies at the
centre of the circle. We say that the angle \(\angle BAC\) is a central angle.
The angle \(\angle DFE\) is called an
inscribed angle because the vertices \(D\), \(F\)
and \(E\) all lie on the circumference
of the circle.
