Let triangle ABC have side lengths AB=13, AC=14, and BC=15.
There are two circles located inside angle BAC
which are tangent to rays AB, AC, and segment BC.
Compute the distance between the centers of these two circles.
My answer see: https://web2.0calc.com/questions/triangle-abc-has-ab-13-ac-14-bc-15-2-circles-in-angle
Given positive integers x and y such that x≠y and
1x+1y=118,
what is the smallest possible value for x+y?
1x+1y=118x+yxy=118xy=18∗(x+y)
AM≥GM
x+y2≥√xyx+y≥2√xy|square both sides(x+y)2≥4xy|xy=18∗(x+y)(x+y)2≥4∗18∗(x+y)x+y≥4∗18x+y≥72
The smallest possible value for x+y is 72
Source: https://www.quora.com/Given-positive-integers-x-and-y-x-does-not-equal-y-and-frac-1-x-frac-1-y-frac-1-12-what-is-the-smallest-possible-value-for-x-y
In general:
1x+1y=1nx+y≥4n
The smallest possible value for x+y is 4n