In triangle ABC, bisectors AA1 and BB1 intersect at point O. Find the ratio of the areas of triangles AOC
| June 24, 2021 | education
In triangle ABC, bisectors AA1 and BB1 intersect at point O. Find the ratio of the areas of triangles AOC and BOC if AC = 8 cm, BC = 6 cm.
The bisectors of a triangle intersect at one point. Since BB1 and AA1 are bisectors, then CO is the bisector of the angle ACB, then the angle OCA = OCB.
In the triangles AOC and BOS, the side of the OS is common.
Saos = AC * OC * SinOCA / 2 = 4 * OC * SinOCA.
Swax = BC * OC * SinOBC = 3 * OC * SinOBC.
Then Saos / Swos = 4 * OC * SinOCA / 3 * OC * SinOBC = 4/3.
Answer: The ratio of the areas of the triangles is 4/3.
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