Question
Download Solution PDFTwo 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Two parallel chords, each of length 8 units, are 6 units apart in a circle.
Formula used:
For a chord of length 2a at a distance d from the center of a circle with radius r:
We use the formula for the distance from the center to the chord:
r2 = d2 + a2
Where a is half the length of the chord.
Calculations:
Let the distance from the center of the circle to one chord be d1, and to the other chord be d2.
Since the chords are 6 units apart, we assume one chord is 3 units above the center, and the other is 3 units below.
Half the length of each chord is a = 8/2 = 4 units.
For the first chord, the distance from the center is 3 units:
⇒ r2 = 32 + 42 = 9 + 16 = 25
⇒ r = √25 = 5 units
∴ The radius of the circle is 5 units.
Last updated on Jun 26, 2025
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