### Video Transcript

The chord π΄π΅ of a circle with
center π has length 28. Suppose the radius ππ· meets π΄π΅
in a right angle at the point πΆ and that πΆπ· has length 9.8. Find the radius of the circle.

The first thing to do is to draw a
sketch. Here we can see our circle with
center π, our chord π΄π΅, our radius ππ·, and the point of intersection πΆ. A good approach for questions like
this is to write down everything we know and then try to form an equation. Recall first that the chord
bisector theorem tells us that any straight line passing through the center of a
circle and intersecting a chord in a right angle must cut that chord in half. In particular, any radius is a
straight line passing though the circleβs center, and so our radius ππ· cuts the
chord π΄π΅ in half. Thus, the segment π΄πΆ has half the
length of the segment π΄π΅, that is, 28 divided by two, which equals 14.

The next thing we know is that π΄π
is also a radius. Letβs call its length π. We can see from the diagram that
the length of ππΆ is the length of ππ· minus the length of πΆπ·. ππ· is a radius and therefore has
length π. And weβre told that the length of
πΆπ· is 9.8. Therefore, ππΆ has length π minus
9.8. Since π΄ππΆ is a right triangle,
we can apply the Pythagorean theorem. We substitute in our values,
multiply out, and simplify. The radius is 292.04 divided by
19.6, which is 14.9.