Two parallel chords of length 8 units each are 6 units away from each other in a circle. What is the radius of the circle in units?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 5.
Let's visualize the problem:
circle with two parallel chords of length 8 units, 6 units apart
Since the chords are parallel and equidistant from the center, the perpendicular distance from the center to each chord is 6/2 = 3 units.
Now, we have a right-angled triangle with one side 3 units and the other side half the length of the chord, which is 8/2 = 4 units.
Using the Pythagorean theorem, we can find the hypotenuse, which is the radius of the circle:
radius2 = 32 + 42
radius2 = 9 + 16
radius2 = 25
radius = 5
Therefore, the radius of the circle is 5 units.