The maximum length of PQ (line passing through the tangent point) = 22 units.
<h3>What is a tangent?</h3>
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,
- Diameter of smaller sphere = d = 2(4) = 8 units
- 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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