Circles
Properties of Chords
Grade 11
Question:
<p>AB is a fixed chord of a circle and XY is any chord having its middle point Z on AB. Analyze: XY is greatest if XY coincides with AB.</p>
<p>(A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1</p>
<p>(B) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1</p>
<p>(C) Statement-1 is true, Statement-2 is false</p>
<p>(D) Both statements are false</p>
Step-by-Step Solution
Key Concept: A chord's length is maximized when its midpoint is closest to the center; if Z is the midpoint of AB, the chord XY through Z is longest when it is AB itself.
<p><strong>Analysis:</strong> For a chord XY with midpoint Z on fixed chord AB, the length of XY depends on the distance of Z from center O. The chord XY is longest when Z is at the midpoint of AB (closest to O if AB is off-center). When XY coincides with AB, both statements are satisfied. Statement-2 is the correct geometric reason.</p>
Correct Answer: A