Question

Точка В не лежит в плоскости АDC. Точки М, Р, К и Е – середины отрезков АВ, ВС, СD и АD соответственно; МК=РЕ=10 см, АС=12 см. Найдите длину отрезка ВD.

Answer 1

Рассмотрим MPKE. В этом 4-х угольнике диагонали MK = PE=10, MP = 6( средняя линия в ΔАВС),
ЕК = 6 (средняя линия в ΔADC), MPKE - параллелограмм. Диагонали равны, значит,этот параллелограмм- прямоугольник . Δ MPK. по т. Пифагора PK^2 = 10^2 - 6^2 = 64, PK = 8 . PK - средняя линия в ΔBDC, значит, BD = 16   

Answer 2

Given Information

- Point V does not lie in the plane ΔADC. - Points M, P, K, and E are the midpoints of segments AB, BC, CD, and AD, respectively. - MK = RE = 10 cm. - AC = 12 cm.

Finding the Length of Segment BD

To find the length of segment BD, we need to use the given information and apply relevant geometric concepts.

Solution

Since M and K are the midpoints of segments AB and CD, respectively, we can conclude that segment MK is parallel to segment AC. This is because the line connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.

Similarly, since P and E are the midpoints of segments BC and AD, respectively, we can conclude that segment PE is parallel to segment BD.

Now, we have two parallel lines, MK and PE, intersected by transversal AC. According to the Intercept Theorem, the lengths of corresponding segments on these parallel lines are proportional.

Therefore, we can set up the following proportion:

MK / AC = PE / BD

Substituting the given values:

10 cm / 12 cm = 10 cm / BD

Simplifying the equation:

BD = (12 cm * 10 cm) / 10 cm = 12 cm

Therefore, the length of segment BD is 12 cm.

Conclusion

The length of segment BD is 12 cm.