Question

Mark the points between the rays $PA$ and $PB$ (both included) which lie at a certain distance, say $d$, from a point $P$, where $PC=d$. How many such points exist?

• A. Infinite points, between the rays $PA$ and $PB$
• B. Only $2$ points, each on the rays $PA$ and $PB$
• C. Only $1$ point, on the ray $PA$
• D. $0$

Answer 1

The correct option is A Infinite points, between the rays $PA$ and $PB$

To locate points which are equidistant from $P$ and at a distance $d$, take a compass, with $P$ as center and radius as $d$, draw an arc which cuts the rays $PA$ and $PB$ at $C$ and $D$ as shown.
Now, all the points on this arc $CD$ are at a distance $d$ from $P$ and, hence, they all meet the given condition.

Therefore, an infinite number of points meeting the given conditions can be marked between $PA$ and $PB$.