Multiple choice

A circle touches the sides $AB$ and $AD$ of a rectangle $ABCD$ at $P$ and $Q$ respectively and passes through the vertex $C$. If the distance of $C$ from chord $PQ$ is $5$ units, then area of the rectangle is :

  1. $45$
  2. $25$
  3. $50$
  4. $75$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the rectangle have sides x and y. The circle passes through C, and touches AB and AD. Using geometry, the distance from C to the chord PQ is related to the dimensions of the rectangle. For a rectangle where a circle touches two sides and passes through the opposite vertex, the area is 25.

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