### Angle of View

**Click
here for a problem description**

The objective is
to maximize the angle*ABC* in the sketch below, where *B* represents
the point from which you are viewing the the billboard *AC*.
Consider the circumcircle of triangle ABC. This circle will meet the
green line in at most two places.

Click for a Circumcircle script.

The angle *ABC* will be a maximum when the circle containing *A*,
*C* and *B *is tangent to the green line. The task then is to
construct a circle given A and C and the green line. This construction is
dealt with in **Apollonius**
problem.

Click here for the GSP script

How can we determine the optimal position of B directly? This follows
directly from the following geometric statement:

Given a circle with tangent *t* meeting the circle at *B* and
with secant *s * meeting the circle at *A * and *C*. Let
*t * and *s * meet at *I* then:
This fact is also the principle underlying the construction used earlier.

**Return**