2025 · Q55
Consider the following for the next two (02) items that follow: A circle M of radius 8 cm touches externally another circle N of radius 16 cm. Let P and Q be the points where the common tangent touches the circles M and N, respectively. What is the length of the common tangent PQ?
Elementary MathematicsCircles
- A16 cm
- B16√2 cm
- C24 cm
- D24√2 cm
Explanation
Equal areas give (1/2)a·3x = (1/2)b·5x = (1/2)c·6x, so 3a = 5b = 6c and a:b:c = 10:6:5. With AB = c, BC = a, CA = b, the ratio AB:BC:CA = 5:10:6, option (b).