Question

Two spheres, one with radius 7 and one with radius 4,

Answer 1

The maximum length of PQ (line passing through the tangent point) = 22 units.

What is a tangent?

A tangent to a circle refers to a straight line which touches the circle at only one point.

In case of spheres too, tangent touches the sphere at one point only.

Now, given:

• Radius of smaller sphere = r = 4 units
• Radius of larger sphere = R = 7 units
• P = point on larger sphere
• Q = point on smaller sphere
• The spheres are tangent to each other, i.e., they touch each other at only 1 point making an angle of 90 degrees.

(refer to the image attached)

To find: The maximum possible length of PQ.

Finding:

• To find the maximum possible length of PQ, we must place the two points on the greatest distance from each other.
• Note that this line PQ will pass through the common point of the two spheres, i.e., their tangents.

• The points on the greatest distance will lie on the ends of the diameter of each sphere.

• Hence, the maximum possible length of PQ = diameter of smaller sphere + diameter of larger sphere.

Since diameter = Twice the radius,

1. Diameter of smaller sphere = d = 2(4) = 8 units
2. Diameter of larger sphere = D = 2(7) = 14 units

Thus, the maximum length of PQ = 8 + 14 = 22 units

To learn more about tangents, refer to the link: brainly.com/question/11067500

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