Chapter 9.6, Problem 27WE

To determine

To find: the equation having a, b and c.

Answer to Problem 27WE

  $c°=b°-a°$

Explanation of Solution

Given:

The figure:

  

Concept used:

The measure of the angle formed by two secants, two tangents or a secant and a tangent drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs.

The measure of an inscribed angle is equal to half the measure of its intercepted arc.

Calculation:

Label the diagram first

  

Let the angle PQR is equal to $x°$

Now applying the theorem, “The measure of the angle formed by two secants, two tangents or a secant and a tangent drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs.” Into the small circle which is inside, we get

  $x°=\frac{1}{2}(b°-a°)$ .

Now applying the theorem, “The measure of an inscribed angle is equal to half the measure of its intercepted arc.” to the larger circle will give,

  $x°=\frac{1}{2}c°$

Now equate both the values of x , we will get

  $\begin{array}{l}\frac{1}{2}c°=\frac{1}{2}(b°-a°)\\ c°=b°-a°\end{array}$