Line AD, perpendicular to the median BM of the triangle ABC, divides the angle BAC in half.
| March 20, 2021 | education
Line AD, perpendicular to the median BM of the triangle ABC, divides the angle BAC in half. Find the AB side if the AC side is 4.
Consider triangles ADM and ABD, they are right-angled, leg AD is common, angles BAD and DAM are equal, therefore, these triangles are equal as right-angled triangles with equal acute angles, so AB = AM. Recall that BM is the median:
AB = AM = fraction, numerator – AC, denominator – 2 = fraction, numerator – 4, denominator – 2 = 2.
AB = AM = AC / 2 = 4/2 = 2
Answer: 2.
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