The segments AB and CD intersect at point O and the intersection point is divided in half.

The segments AB and CD intersect at point O and the intersection point is divided in half. CO = 5cm, BD = 6cm, and the perimeter of triangle AOC is 18cm. Find the length of segment AB.

By condition, two segments AB and CD intersect at point O (see figure).

At the point of intersection, the segments are halved.

So CO = OD, AO = OB.

It is known that CO = 5 cm, which means OD = 5 cm.

Also the angles AOC and BOD are equal since they are vertical.

By the first sign of equality of triangles, triangles AOC and BOD are equal.

Therefore CA = BD = 6 cm.

Perimeter of triangle AOC = 18 cm.

Let’s find the length of AO.

AO = 18 – 5 – 6 = 7 cm.

AB = AO + OB = 7 + 7 = 14 cm.

Answer: AB = 14 cm.