I need help answering this question.Point A is outside a circle and AB and AC are tangent to the circle at B and C, respectively. Point P and R are...

We draw the figure.

Let A be
any point  out side a circle with centre O and radius
r.

Since AB and AC are two external tangents to the circle 
at points B  and C, the lengths of tangents are equal. So AB= AC. But AB = 20 given.
Therefore AC = 20.

PQR is a tangent to the circle at Q. P
is on AB and R is on AC. Therefore P is an external point to the circle . PB and PQ are
two external tangents to the circle.

So PB = PQ
....(1)

Similarly RC = RQ......(2)  as RC and RQ, as RC and
RQ are tangets to the circle from an external point.

Add AP
to both sides of eq(1):

AP+PB = AP+PQ.
Or

AB = AP+PQ........(3).

Add
AR to both sides of eq(2):

AR+RC =
AR+RQ.

AC =
AR+RQ............(4).

Add eq (3) and eq
(4):

AB+AC = AP+PQ+AR+ RQ.
Or

AB+AC = AP+PQ+QR +AR

AP+AC
= AP+ PR+AR = Perimeter of the triangle APR.

20+20 = 40
 Perimeter of triangle APR

Therefore the perimeter of
triangle APR =
40.

Perimeter