Question

The big semi-circle has radius 4.
The big full circle has radius 2 and is tangent to the semi-circle and its diameter.
The smaller circle has radius x and is tangent to big full circle, tangent to the semi-circle and tangent to the diameter of the semi-circle.

Find x

Answer 1

Would x just be 1?

Answer 2

What made you decide that x=1?

Answer 3

Hm. Well I was just looking at how big it looks like it would be, but you're right. It can't be 1.

Answer 4

i think what Dr. Saab means is: prove it is what you think it is...

Answer 5

Why it will not be 1?
Since the radius remains the same throughout.

we can measure that from the straight vertical line from the centre of the circle.

Thus, since x is the radius too therefore x is 1 as well. D:

Answer 6

@saifoo.khan Yeah, that's where I was going at first too. I saw that it looked like 1 based on the measurement. IDK.

Answer 7

I think this applies here:
http://www.demotivation.us/media/demotivators/demotivation.us_RULE-OF-MATH-If-it-seems-easy-youre-doing-it-wrong.-_133804518015.jpg

Answer 8

Haha, touché.

Answer 9

how do you type that e with that thingy above it?

Answer 10

im getting x = 0.75

Answer 11

@thechocoluver445 : ;)

@dpaInc : in that photo? that inverted E?

Answer 12

touche' somtin like that//

Answer 13

Some computers have this option.. you use ' first then type e.

Answer 14

What's the answer of this trig problem?

Answer 15

i dunno... yet...

Answer 16

@thechocoluver445, now that I revised my computation, I think that x=1.
I will wait a couple of days to see if someone comes up with a proof that x=1 and then I will post my proof.

Answer 17

quick question..is this spherical trigonometry?

Answer 18

What do you mean by spherical trigonometry?

Answer 19

i mean when triangles are on circles..making their sides curved..idk if that applies here just making sure?

Answer 20

My solution involves only equations of circles and basic algebra.

Answer 21

the radius of the semi-circle=4
and since the big circle sits perfectly so that its diameter is on the y-axis, its radius is part of the radius of the semicircle, and since the small cirlce is tanget to the big circle, the semicircle and the x-axis, it's diameter is part of the radius of the semicircle so:

4=(radius of big circle)+(diameter of the small circle)
4=(radius of big circle)+(2)(radius of small circle)
4=2+2x
x=1

Answer 22

@Tushara i'd guess you've just assumed things..i.e. everything is symmetrical and should follow your eqns..if you assume all that,,why not construct a perpendicular from the center of smaller circle to the y axis and say that it bisects (0,0) and (0,2),,which automatically gives x=1//so you see what am intending to say..hmm
there must be a good solution to this,,i mean better :P

Answer 23

true^ :)

Answer 24

maybe i just got it,,hold on,,i'll post it..

Answer 25

so we have this :
(4-x)^2 - (x^2) = (2+x)^2 - (2-x)^2
=>x=1
phew!!
i hope i didnt make any mistakes..