Bisector AK is drawn in triangle ABC. Find K and KC if AB = 10cm, AC = 12cm, BC = 11cm.
| September 1, 2021 | education
1. We take the length of the segment BK as x (centimeters), then CK = (11 – x) centimeters.
2. According to the properties of the bisector, it divides the side to which it is drawn into segments that are proportional to the other two sides. Based on this, we make up the proportion:
AB / x = BC (11-x).
10 / x = 11 / (11- x)
110 – 10x = 12x;
22x = 110;
x = 5.
BK = 5 centimeters.
CK = 11 – 5 = 6 centimeters.
Answer: BK = 5 centimeters, CK = 6 centimeters.
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