Circles · Class 9 · CBSE Mathematics
If a line intersects two concentric circles with center O at points A, B, C, and D in that order, which of the following is always true regarding the…
Practice question from Circles (Class 9 · CBSE Mathematics), with the correct answer and a step-by-step solution.
medium · MCQ · Q-7741EF
If a line intersects two concentric circles with center O at points A, B, C, and D in that order, which of the following is always true regarding the lengths of line segments?
- A.AB = CDCorrect answer
- B.AC = BD
- C.AD = BC
- D.AB > CD
Solution
Draw a perpendicular from the center to the line. Let it meet the line at . Since the perpendicular from the center to a chord bisects the chord, we have (for the outer circle) and (for the inner circle). Subtracting the two gives , which means .
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