The bisectors of the angles A and B of the lateral side AB of the trapezoid ABCD meet at point P.
| March 19, 2021 | education
The bisectors of the angles A and B of the lateral side AB of the trapezoid ABCD meet at point P. Find AP if AB = 13, BP = 12.
By the property of the bisectors of the trapezoid drawn from the vertices of the lateral side, a right angle is formed at the point of their intersection. Then the triangle APB is rectangular, from which, according to the Pythagorean theorem, we determine the length of the leg AP.
AP ^ 2 = AB ^ 2 – BP ^ 2 = 13 ^ 2 + 12 ^ 2 = 169 – 144 = 25.
AR = √25 = 5 cm.
Answer: The length of the AP segment is 5 cm.
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