Djmathman's 100 Geometry Problems

by First, Nov 24, 2016, 3:48 PM

2013 AMC 10A #23 wrote:
on 100 Geometry Problems]In $\triangle{ABC}, AB=86$ and $AC=87$. A circle with center A and and radius $AB$ intersects $\overline{BC}$ at $B$ and $X$. Also $\overline{BX}$ and $\overline{CX}$ have integer lengths. What is BC?
Solution
AIME Unused wrote:
In the figure, $ABC$ is a triangle and $AB=30$ is a diameter of the circle. If $AD=\frac{AC}{3}$ and $BE=\frac{BC}{4}$, then what is the area of $\triangle{ABC}$?

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Solution to AIME Unused

by First, Nov 24, 2016, 4:09 PM

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I was being an idiot here is the final touch to the 2nd problem:
Final Touch

by First, Nov 24, 2016, 4:21 PM

To share with readers my favorite problem I came across today :) (Shout for contrib.)

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  • Let $ ABC$ be an equilateral triangle of side length $ 1$. Let $ D$ be the point such that $ C$ is the midpoint of $ BD$, and let $ I$ be the incenter of triangle $ ACD$. Let $ E$ be the point on line $ AB$ such that $ DE$ and $ BI$ are perpendicular. $ \

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