# Difference between revisions of "1964 AHSME Problems/Problem 36"

## Problem

In this figure the radius of the circle is equal to the altitude of the equilateral triangle $ABC$. The circle is made to roll along the side $AB$, remaining tangent to it at a variable point $T$ and intersecting lines $AC$ and $BC$ in variable points $M$ and $N$, respectively. Let $n$ be the number of degrees in arc $MTN$. Then $n$, for all permissible positions of the circle: $\textbf{(A) }\text{varies from }30^{\circ}\text{ to }90^{\circ}$ $\textbf{(B) }\text{varies from }30^{\circ}\text{ to }60^{\circ}$ $\textbf{(C) }\text{varies from }60^{\circ}\text{ to }90^{\circ}$ $\textbf{(D) }\text{remains constant at }30^{\circ}$ $\textbf{(E) }\text{remains constant at }60^{\circ}$ $[asy] pair A = (0,0), B = (1,0), C = dir(60), T = (2/3,0); pair M = intersectionpoint(A--C,Circle((2/3,sqrt(3)/2),sqrt(3)/2)), N = intersectionpoint(B--C,Circle((2/3,sqrt(3)/2),sqrt(3)/2)); draw((0,0)--(1,0)--dir(60)--cycle); draw(Circle((2/3,sqrt(3)/2),sqrt(3)/2)); label("A",A,dir(210)); label("B",B,dir(-30)); label("C",C,dir(90)); label("M",M,dir(190)); label("N",N,dir(75)); label("T",T,dir(-90)); [/asy]$

## Solution

E

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