Question:medium
If the line \( x \cos \alpha + y \sin \alpha = p \) represents the common chord of the circles \( x^2 + y^2 = a^2 \) and \( x^2 + y^2 + b^2 = 2b \), where \( a > b \), where A and B lie on the first circle and P and Q lie on the second circle, then \( AP \) is equal to:
If the line \( x \cos \alpha + y \sin \alpha = p \) represents the common chord of the circles \( x^2 + y^2 = a^2 \) and \( x^2 + y^2 + b^2 = 2b \), where \( a > b \), where A and B lie on the first circle and P and Q lie on the second circle, then \( AP \) is equal to:
Show Hint
To find the length of a common chord, use geometric properties of the intersecting circles.
Updated On: Mar 25, 2026
- \( \sqrt{a^2 + p^2} + \sqrt{b^2 + p^2} \)
- \( \sqrt{a^2 - p^2} + \sqrt{b^2 - p^2} \)
- \( \sqrt{a^2 + p^2} - \sqrt{b^2 + p^2} \)
- \( \sqrt{a^2 - p^2} - \sqrt{b^2 - p^2} \)
Show Solution
The Correct Option is B
Solution and Explanation
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