2021 Fall AMC 10A Problems/Problem 15
Isosceles triangle has
, and a circle with radius
is tangent to line
at
and to line
at
. What is the area of the circle that passes through vertices
,
, and
Solution 1
Let the center of the first circle be By Pythagorean Theorem,
Now, notice that since
is
degrees, so arc
is
degrees and
is the diameter. Thus, the radius is
so the area is
- kante314
Solution 2 (Similar Triangles)
Because circle is tangent to
at
. Because O is the circumcenter of
is the perpendicular bisector of
.
Solution in Progress
~KingRavi
See Also
2021 Fall AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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