Segments AB and CD intersect at point O and the intersection is halved. In this case, CO is exactly 5 cm

| January 28, 2021 | education

Segments AB and CD intersect at point O and the intersection is halved. In this case, CO is exactly 5 cm, BD is 6 cm, and the perimeter of the triangle AOC is 18 cm. Find the length of the segment AB.

Consider the DOB triangle and the AOC triangle. The DOB angle is equal to the AOC angle, since the vertical angles are at the intersection of two straight lines. Equal sides lie opposite equal angles. Side DB = AC = 6 cm. In the AOC triangle, the CO side is 5 cm, the AC side is 6 cm, the perimeter of the AOC triangle is 18 cm. The perimeter of the triangle is equal to the sum of the lengths of its three sides.

1) Find the length of the side AO, triangle AOC.

18 – (6 + 5) = 18 – 11 = 7 centimeters.

2) Find the length of the segment AB.

7 * 2 = 14 centimeters.

Answer: The length of the segment AB is 14 centimeters.



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