The diagonals of a square meet at O. The bisector of angle OAB meets BO and BC at N and P respectively. The length of NO is 24. How long is PC?
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
The diagonals of a trapezium divide it into four parts. Can you
create a trapezium where three of those parts are equal in area?
For example if $OP$ happened to be $2/3$ of the radius then
$OP'$ would be $3/2$ of the radius.
You can use the interactivity below to help you explore how the
positions of a pair of points relate to each other.
Once you have a feel for that, leave the interactivity and go on
to the main problem which is best done by drawing sketches on
In the diagram above, $P$ and $P'$ are a connected pair, and $Q$
and $Q'$ the same, both pairs behaving like the points in the
Now for the problem : The radius of the circle is 10 units, $OP$
is 8 units and $OQ$ is 6 units.
If the distance $PQ$ is 5 units what is the distance $P'Q'$?