vipulgoyal wrote:
In the figure shown, the circle has center O and radius 50, and point P has coordinates (50,0). If point Q (not shown) is on the circle, what is the length of line segment PQ ?
(1) The x-coordinate of point Q is - 30.
(2) The y-coordinate of point Q is - 40
The equation of a circle with center (0,0) and radius r is x²+y² = r².
Here, r=50.
Thus, x²+y² = 50².
Statement 1: The x-coordinate of point Q is - 30.
Whether Q is in quadrant II or in quadrant III, the length of PQ will be the same.
Since the equation of the circle is known, Q's y-coordinate in each quadrant can be determined, allowing us to calculate the length of PQ.
SUFFICIENT.
Statement 2: The y-coordinate of point Q is - 40.
The figure above shows that PQ can be different lengths.
INSUFFICIENT.
The correct answer is
A.
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