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In the diagram below, chord DF is parallel to the diameter AC. The length of DF is 20 cm and the length of AC is 28 cm. What is the distance, in centimeters, from B, the center of the circle, to E, the midpoint of DF?
Title
Distance from chord to the center
Your Result
Correct
Difficulty
Hard
Your Pace
0:02
Others' Pace
1:18
Video Explanation
Text Explanation
The answer is C. Since we know the diameter of the circle is 28, this means that the radius of the circle is half of this, or 14. We can construct a line between B and D that would be a radius of the circle and would create a right triangle with chord and the line between the center and the chord. The hypotenuse of this triangle (BD) would equal 14 because it is a radius and DE = 10 because it is half the length of chord DF.
We can use the Pythagorean Theorem to solve for the length of BE:
So our answer is C.
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