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Results tagged with triangles
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user 494920
1
vote
0
answers
111
views
A circle is inscribed in a triangle, with three other circles in the corner regions. The rad...
Originally posted at MSE.
A circle with integer radius $R$ is inscribed in a triangle. Three other circles with integer radii $a,b,c$ are each tangent to the large circle and two sides of the triangl …
- 3,507
5
votes
The vertices of a triangle are three random points on a unit circle. The side lengths are, i...
A proof from pure geometry
On a unit circle with centre $O$, draw parallel chords $PQ$ and $P'Q'$ such that $PQ'\perp P'Q$. Chord $MN$ is parallel to $PQ$ and passes through $R$, the intersection of $ …
- 3,507
13
votes
8
answers
1k
views
The vertices of a triangle are three random points on a unit circle. The side lengths are, i...
The vertices of a triangle are three unifomly random points on a unit circle. The side lengths are, in random order, $a,b,c$.
There is a convoluted proof that $P(ab>c)=\frac12$. But since the probabil …
- 3,507