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Three spheres are tangent to a plane at the vertices of a triangle and are tangent to each other. find the radii of these spheres if the sides of the triangle are 6, 8, and 10.
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May 28, 2019
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Three spheres are tangent to a plane at the vertices of a triangle and are tangent to each other. find the radii of these spheres if the sides of the triangle are 6, 8, and 10.
Mathematics
high-school
Holstebroe
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Three spheres are tangent to a plane at the vertices of a triangle and are tangent to each other. Denote the points where spheres are tangent to the lane A, B, C. You get a triangle ABC with lengths of sides 6, 8 and 10. Denote
the projections of the tangent points between spheres on the pane.
Then
and
.
Add all these three equations:
and substract each equation from
:
.
Then
are spheres' radii.
Rozwel
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Jun 1, 2019
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Rozwel
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