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Question
Assertion (A): In the given figure, chord AB = 8 cm, diameter CD = 20 cm, then length of OP = 10 cm.
Reason (R): OP = `sqrt(OA^2 - AP^2)` and CP = OC + OP.
Options
A is true, R is false.
A is false, R is true.
Both A and R are true and R is the correct reason for A.
Both A and R are true and R is the incorrect reason for A.
MCQ
Assertion and Reasoning
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Solution
A is false, R is true.
Explanation:
The assertion is false because the radius is $10\text{ cm}$ and $\text{AP}$ is $4\text{ cm}$, meaning the actual length is:
OP = `sqrt(10^2 - 4^2)`
∴ OP = `sqrt84` cm
The reason is a true statement as it correctly applies the Pythagorean theorem to the right-angled triangle and accurately identifies the line segment addition from the diagram.
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