Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measure of arc FD.

Circle C is shown. Line segments E C and D F are radii. Lines are drawn from points E and D to point F to form chords E F and D F. Tangents E G and D G intersect at point G outside of the circle. Angle E G D is 60 degrees and angles G E C and G D C are right angles. The lengths of E F and D F are congruent.

Which statements about the arcs and angles are true? Select three options.

∠EFD ≅ ∠EGD
∠EGD ≅ ∠ECD
Arc E D is-congruent-to arc F D
mArc E F = 60°
mArc F D = 120°

Step-by-step explanation:

In Quadrilateral GECD,

In Triangle EFD,

Similarly, In Triangle GED

Finally, Arc ED is-congruent-to arc F D

The first, third and last options are true.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

7

step-by-step explanation: