Question

Three circles with centers A, B, and C are externally tangent to each other as shown in the figure. Lines EG and DG are tangent to circle C at points F and D and intersect at point G. If each circle has a diameter of 6 inches, find the length of DG and the area enclosed by lines FG and GD, and arc FD. :) help pleaaaaaaaase

Answer 1

damn...tough one for me :(

Answer 2

ED = 6+6+6 = 18 inches
DG^2 = EG^2 - ED^2, how to find EG is the question...

Answer 3

I can't solve this one too T^T

Answer 4

ahh easy, finding DG, stay tuned

Answer 5

draw a line from C to F

Answer 6

this will make a right angle at F and CF = the radius 3 inches, right?

Answer 7

yes? the radius is 3 in.

Answer 8

EF^2 + FC^2 = EC^2 , pythag.theorem, right?

Answer 9

EF = SQRT (EC^2 - CF^2)
= SQRT( 15^2 - 3^2 )
= SQRT ( 216)
right ?

Answer 10

what do u say?

Answer 11

right.... ^^ the next problem is to find the measure of the bigger traingle (i mean GED) :3

Answer 12

i think find first DG?
do you agree that DG = FG ? it's one of the properties of circles and tangents...

Answer 13

DG = FG? I guess? haha. I'm a little bit confused. sorry :>

Answer 14

say that x = DG = FG
we can construct the following statement based on pythag.theo
bear in mind that the angle GDC is Right Angle
and EG = EF +x, we already found EF = SQRT (216) above

Answer 15

(EF + x)^2 = x^2 + ED^2
substitue EF with SQRT(216) and ED with 18 and find x - quadratic equation, know how to solve that?

Answer 16

yes.. yes.. i get it now XD

Answer 17

\[DG = \sqrt{13.5}\]

Answer 18

yes. i got it!! thankss

Answer 19

great, am not sure how to calculate the shaded area, sorry...I'll keep thinking but cant promise to have an answer

Answer 20

I'll give you the steps for further work, you'll need to use your textbook to find the formulas though
1. draw a line from C to G,
2. find the angle DCG using sin, cos, tan ... you already know CD = 3 and DG = SQRT 13.5
3. using the above 2 steps now you can find the length of CG
4. using sin/cos/tan and the 3 sides of the triangle CDG find the area of it
5. this will be the same as the area of the mirroring triangle CFG
6. find the area of the segment CFD, you know the angle at C and u know CD = 4 and CD = 3
7. subtract the area in 6 above from the sum of the area of the 2 triangles you worked out above in points 4 and 5
8. this will be the area of the shaded part.

Answer 21

correction to step 6 above, sorry... CD = 3 and CF = 3