In the ABC triangle, the BK segment is the height, the AM segment is the bisector, BK is 36cm, AB: AC = 6: 7.

| January 7, 2021 | education

In the ABC triangle, the BK segment is the height, the AM segment is the bisector, BK is 36cm, AB: AC = 6: 7. From point M, the perpendicular MD is dropped to the AC side. Find MD

By the property of the bisector, it divides the side of the triangle into segments proportional to the adjacent sides.
AB / BM = AC / CM.
BM * AC = AB * CM.
AB / AC = BM / CM = 6/7.
Let the length of the segment BM = 6 * X, then CM = 7 * X, and the segment BC = BM + CM = 13 * X.
Consider two right-angled triangles, BKC and MDC, in which the angle C is common, and the angle CMD = CBK as the corresponding angles at the intersection of parallel lines BK and MD secant BC.
Then the BKC and MDC triangles are similar in two angles.
BK / MD = BC / MC.
36 / MD = 13 * X / 7 * X.
MD = 36 * 7/13 = 19.38 cm.
Answer: MD segment = 19.38 cm.



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