1974 AHSME Problems/Problem 23
Problem
In the adjoining figure and
are parallel tangents to a circle of radius
, with
and
the points of tangency.
is a third tangent with
as a point of tangency. If
and
then
is
Solution
Drop the perpendicular from to
and let the foot be
. Note that
is a rectangle. Also, from Two Tangents,
and
, so
. Therefore, from the Pythagorean Theorem on
,
. We now see that
.
See Also
1974 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |