Cycle Center o with pq parallel to RS. straight line GOF is perpendicular to PQ. RS is equal to 80 units PQ is equal to 60 units and radius of the cycle is 50 units. calculate the distance FG between the chords PQ and RS

Answer 1

First, we need to find the distance between the center of the circle (O) and the line GOF. This distance is equal to the radius of the circle, which is 50 units.

Next, we can consider triangle OGF, which is a right-angled triangle since GOF is perpendicular to PQ. We know the length of one side (OF = 50 units) and we need to find the length of the hypotenuse (OG = radius of the circle + the required distance FG).

Using the Pythagorean theorem, we can calculate the length of the hypotenuse OG:
OG^2 = OF^2 + FG^2
=> (50 + FG)^2 = 50^2 + 60^2
=> FG = sqrt(50^2 + 60^2) - 50

FG = sqrt(2500 + 3600) - 50
FG = sqrt(6100) - 50
FG = 78.08 - 50
FG ≈ 28.08 units

Therefore, the distance FG between the chords PQ and RS is approximately 28.08 units.