First, we need to find the distance between the chords PQ and RS. Since PQ is 60 units long and RS is 80 units long, we can calculate the distance between the chords by using the formula for the distance between two chords in a circle:
Distance between chords = 1/2 * √[(2r - PQ - RS)(2r + PQ + RS)]
Plugging in the values:
Distance between chords = 1/2 * √[(2(50) - 60 - 80)(2(50) + 60 + 80)]
Distance between chords = 1/2 * √[(100 - 60 - 80)(100 + 60 + 80)]
Distance between chords = 1/2 * √[(20)(240)]
Distance between chords = 1/2 * √[4800]
Distance between chords = 1/2 * 69.28
Distance between chords = 34.64 units
Next, we need to find FG, which is part of a right triangle formed by the radius of the circle, FG, and the line GOF.
Using the Pythagorean theorem, we can find FG:
r^2 = FG^2 + GO^2
50^2 = FG^2 + (34.64)^2
2500 = FG^2 + 1198.88
FG^2 = 1301.12
FG = √1301.12
FG ≈ 36.09 units
Therefore, the distance FG between the chords PQ and RS is approximately 36.09 units.
Given :circle centre O, with PQ||RS. straight line GOF is perpendicular to PQ. RS =80 units, PQ =60 units and the radius of the circle is 50 units. calculate the distance FG between the chords PQ and RS.
1 answer
1 answer