6

Part of 2017 AIME Problems

Problems(2)

Wot n' Intersection

Source: 2017 AIME I #6

A circle is circumscribed around an isosceles triangle whose two congruent angles have degree measure

x

. Two points are chosen independently and uniformly at random on the circle, and a chord is drawn between them. The probability that the chord intersects the triangle is

\frac{14}{25}

. Find the difference between the largest and smallest possible values of

x

2017 AIME IWot n

Native Sum of all n such that sqrt of quadratic is integer

Source: 2017 AIME II #6

Find the sum of all positive integers

n

\sqrt{n^2+85n+2017}

quadraticsAMCAIMEAIME II