In the triangle ABC AB = BC, AC = 16 cm, BD-median. Find the distance from point A to line BD.
| February 15, 2021 | education
In the triangle ABC AB = BC, AC = 16 cm, BD-median. Find the distance from point A to line BD. Find the distance from point C to a straight line passing through point A parallel to BD.
The ABC triangle is isosceles, since AB = BC, then the median ВD is also the height of the triangle, and therefore ВD is perpendicular to the base of the AС.
Since, by condition, AK is parallel to ВD, then, by the property of parallel lines, AK is perpendicular to AC, then the AC segment is the shortest distance from point C to straight AK.
AC = 16 cm. AD = AC / 2 = 16/2 = 8 cm.
Answer: From point A to straight line AK 8 cm, from point C to straight line AK 18 cm.
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