Difference between revisions of "1975 AHSME Problems/Problem 24"
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| + | ==Problem== | ||
| + | In triangle <math>ABC</math>, <math>\angle C = \theta</math> and <math>\angle B = 2\theta</math>, where <math>0^{\circ} < \theta < 60^{\circ}</math>. The circle with center <math>A</math> and radius <math>AB</math> intersects <math>AC</math> at <math>D</math> and intersects <math>BC</math>, extended if necessary, at <math>B</math> and at <math>E</math> (<math>E</math> may coincide with <math>B</math>). Then <math>EC = AD</math> | ||
| + | <math> | ||
| + | \textbf{(A)}\ \text{for no values of}\ \theta \qquad | ||
| + | \textbf{(B)}\ \text{only if}\ \theta = 45^{\circ} \\ | ||
| + | \textbf{(C)}\ \text{only if}\ 0^{\circ} < \theta \leq 45^{\circ} \qquad | ||
| + | \textbf{(D)}\ \text{only if}\ 45^{\circ} \leq \theta \leq 60^{\circ} \\ | ||
| + | \textbf{(E)}\ \text{for all}\ \theta\ \text{such that}\ 0^{\circ} < \theta < 60^{\circ} | ||
| + | </math> | ||
| + | |||
| + | ==Solution== | ||
| + | nothing yet :( | ||
| + | |||
| + | ==See Also== | ||
| + | {{AHSME box|year=1975|num-b=23|num-a=25}} | ||
| + | {{MAA Notice}} | ||
Revision as of 16:54, 19 January 2021
Problem
In triangle 
, 
and 
, where 
. The circle with center 
and radius 
intersects 
at 
and intersects 
, extended if necessary, at 
and at 
( may coincide with ). Then 
Solution
nothing yet :(
See Also
| 1975 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
