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PICTURE ONE: $\angle CAB=30°$ and $AB=2BC$ Assuming $\angle ACB \ne 90°$. We find a point $D$ lying on ray $AC$ such that $\angle BDA=90°$. Because $\angle CAB=30°$ and $\angle BDA=90°$, $AB=2BD$ …

Of course a circle is an example. Is there any other example other than a circle? A chord is the line segment joining two points on a curve.

We are given a rectangle. Its adjacent sides are $m$ and $n$ ($m \geq n$). We need to find the largest semicircle in this rectangle. How can we find it? EDIT: Beware of such situations!!

Ruler postulate: For every pair of points $P$ and $Q$ there exists a real number PQ, called the distance from $P$ to $Q$. For each line $l$ there is a one-to-one correspondence from $l$ to $R$ such t …

But I can't construct a non-Euclidean model which satisfies all axioms (taxicab geometry is similar). Any reference is cordially appreciated. …

Apologies in advance if this is off-topic. Let $r$ denote the length of $CR$. Applying the ruler postulate, we can assign the numbers $0$ and $1$ to $P$ and $Q$, respectively. According to the ruler p …