What is the length of the common tangent PQ?
Consider the following for the next two (02) items that follow :<br>A circle M of radius 8 cm touches externally with another circle N of radius 16 cm. Let P, Q be the points where the common tangent touches the circles M and N respectively.
- A. 16 cm
- B. 16\sqrt{2} cm ✓
- C. 24 cm
- D. 24\sqrt{2} cm
Correct Answer: B. 16\sqrt{2} cm
Explanation
For externally touching circles, the distance between centers d = r_1 + r_2 = 8+16 = 24. The direct common tangent PQ = \sqrt{d^2 - (r_2 - r_1)^2} = \sqrt{24^2 - 8^2} = \sqrt{576 - 64} = \sqrt{512} = 16\sqrt{2} cm.
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