Difference between revisions of "2007 AMC 12B Problems/Problem 3"
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<math>\mathrm {(A)} 35 \qquad \mathrm {(B)} 40 \qquad \mathrm {(C)} 45 \qquad \mathrm {(D)} 50 \qquad \mathrm {(E)} 60</math> | <math>\mathrm {(A)} 35 \qquad \mathrm {(B)} 40 \qquad \mathrm {(C)} 45 \qquad \mathrm {(D)} 50 \qquad \mathrm {(E)} 60</math> | ||
==Solution== | ==Solution== | ||
− | Since triangles <math>ABO</math> and <math>BOC</math> are isosceles, <math>\angle ABO=20^o</math> and <math>\angle OBC=30^o</math>. Therefore, <math>\angle ABC=50^o</math>, or <math>\ | + | Since triangles <math>ABO</math> and <math>BOC</math> are isosceles, <math>\angle ABO=20^o</math> and <math>\angle OBC=30^o</math>. Therefore, <math>\angle ABC=50^o</math>, or <math>\mathrm{(D)}</math>. |
==See Also== | ==See Also== |
Latest revision as of 17:05, 1 January 2021
Problem
The point is the center of the circle circumscribed about triangle , with and , as shown. What is the degree measure of ?
Solution
Since triangles and are isosceles, and . Therefore, , or .
See Also
2007 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 2 |
Followed by Problem 4 |
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All AMC 12 Problems and Solutions |
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