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How the Altitude Divides the Hypotenuse

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show expression(s) for:
legs
hypotenuse
AD
≈
0.92
AC
≈
1.56
DC
≈
0.64
AB
≈
1.20
AC×AD
≈
1.20
BC
≈
1
AC×DC
≈
1.00
Draw the altitude to the hypotenuse of a right triangle. Then each leg is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to that leg:
AB=
AC×AD
and
BC=
AC×DC
. Also, the length of the altitude is the geometric mean of the two segments:
BD=
AD×DC
.
Drag the orange points to change the figure.
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