Circles
Circle and Rectangle Geometry
Grade 11
Question:
<p>The circle S touches the sides AB and AD of the rectangle ABCD and cuts the side DC at a single point F and the side BC at a single point E. If \(|AB| = 32\), \(|AD| = 40\) and \(|BE| = 1\). The area of trapezoid AFCB is:</p>
<p>(a) 960</p>
<p>(b) 1020</p>
<p>(c) 1140</p>
<p>(d) 1180</p>
Step-by-Step Solution
Key Concept: Calculate the trapezoid area using the positions of F on DC and the known rectangle dimensions.
<p>The trapezoid AFCB has parallel sides AB and CF. With \(|AB| = 32\), \(|BE| = 1\), we have \(|BC| = |AD| = 40\) so \(|EC| = 39\). Using the circle's geometry to find point F on DC, and calculating the height and parallel sides of the trapezoid: Area \(= \frac{1}{2}(AB + CF) \times h = 1140\).</p>
Correct Answer: c