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

Segments AB and CD intersect at point O and the intersection point is divided in half. AO = 25 cm, CD = 62 cm, and the perimeter of triangle AOC is 102 cm. Find the length of side BD. Give your answer in centimeters.

At the intersection of the segments, we got two triangles AOC and BOD. They are equal in the first sign of equality of triangles (on two sides and the angle between them).

Consider the AOC triangle:

PAOC = 102 cm;

AO = 25 cm, CO = ½ CD = 62/2 = 31 cm.

AC = 102 – (25 +31) = 46 cm;

BD = AC = 46 cm.

Answer: BD = 46 cm.