Difference between revisions of "1956 AHSME Problems/Problem 10"
(Created page with "==Problem== A circle of radius <math>10</math> inches has its center at the vertex <math>C</math> of an equilateral triangle <math>ABC</math> and passes through the other two...") |
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passes through the other two vertices. The side <math>AC</math> extended through <math>C</math> intersects the circle | passes through the other two vertices. The side <math>AC</math> extended through <math>C</math> intersects the circle | ||
at <math>D</math>. The number of degrees of angle <math>ADB</math> is: | at <math>D</math>. The number of degrees of angle <math>ADB</math> is: | ||
| − | (A) 15 (B) 30 (C) 60 (D) 90 (E) 120 | + | <math>(A) 15 (B) 30 (C) 60 (D) 90 (E) 120</math> |
<asy> | <asy> | ||
import olympiad; | import olympiad; | ||
Revision as of 20:01, 5 May 2019
Problem
A circle of radius 
inches has its center at the vertex 
of an equilateral triangle 
and
passes through the other two vertices. The side 
extended through intersects the circle
at 
. The number of degrees of angle 
is:
![[asy] import olympiad; draw(circle((0,0),10)); dot((0,0)); label("C", (1,-1)); dot((5,5sqrt(3))); dot((-5,-5sqrt(3))); draw((-5,-5sqrt(3))--(5,5sqrt(3))); label("A",(6,5sqrt(3)+1)); label("D",(-6,-5sqrt(3)-1)); draw((0,0)--(10,0)); label("10",(1.5,2.5sqrt(3)+1)); dot((10,0)); label("B",(11,-1)); draw((5,5sqrt(3))--(10,0)); draw(anglemark((10,0),(0,0),(5,5sqrt(3)),60)); label( "60°", (2.5,1.25)); draw((-5,-5sqrt(3))--(10,0)); draw(anglemark((10,0),(-5,-5sqrt(3)),(5,5sqrt(3)),60)); label("?",(-2.5,-5sqrt(3)+2.5)); [/asy]](http://latex.artofproblemsolving.com/4/3/a/43a88a9e44910c5eb3eb9802827b2e73ad093ad2.png)
is an equilateral triangle, so ∠ must be 
°. Since is on the circle and ∠ contains arc 
, we know that ∠ is 
° 
.
