An easy geometrical problem

Geometry Level 2

In square $ABCD$ , point $M$ , $N$ , $O$ and $P$ are on sides $AB$ , $BC$ , $CD$ and $AD$ respectively. Line $MO$ and $NP$ intersects at point $X$ . $PO$ and $DX$ intersects at point $Y$ . If $\frac{DY}{OY}=\frac{PY}{YX}$ , $AB=10$ and $AM=1$ , what is the value of $CN+AP+CO$ ?

17 26 19 23

1 solution

Arifin Ikram
Sep 19, 2019

Given, $\frac{DY}{OY}=\frac{PY}{YX}$

We can write this as $DY * YX=PY * OY.$

According to the inverse theorem of Power Of Point we get that quadrilateral $PXOD$ is in a circle. So $\angle PXO=90^\circ$ . If so, obviously the value of $CN+AP+CO+AM$ will be 20(half of the perimeter).

So $CN+AP+CO$ = $\boxed{19}$ .

An easy geometrical problem

1 solution

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