SRL Archive - Mathematics

Find the radius, the perimeter(solid blue) is 25.

I'm TA for my old math teacher, and he asked me to find out the answer to this for his honors geometrey class, just for old times sake(we always used to do these little challenges), and this time i'm stumped. He also doesn't know how to do this, so he has me, and every other math teacher working on this. I figured you guys are smarter :)

does p = the inscribed angle?

It looks like you made it go a little past it, but it's possible you were just being sloppy.

perimeter i believe

From: Capricorn
does p = the inscribed angle?

It looks like you made it go a little past it, but it's possible you were just being sloppy.

p = entire perimiter excluding dotted line, yes i was being sloppy :)

radius is about 4.224. diam is 8.448
to figure it out start with .5 pi X + sqrt (X^2 -49) + 7 = 25
eventually you get X = 8.448ish. from there you test by plugging it in for X.
8.448 pi / 2 + 7 + sqrt (( 8.448^2 )-( 7^2 )) (which gives you your your other leg of 4.729) = 25 almost exact.

could you post a source of the formula/ website where i can learn how, :)

it looks right, but i need to make sure + understand all of it

i used pathagorean. but started off with half of circumference plus the two sides = 25 (perim). from there its algebra

/facedesk

i can't beileve i havn't seen this D:

thanks for the help :D

yeah

Well.. here's how I did it (finally without errors…):

Call the unlabeled side of the triangle x (the one that's not the diameter of the circle)
then the perimeter 25 = PI*r + 7 + x
PI * r = 18 - x – rearranging
2r = (36 - 2x) / PI – 2r is the length of the hypotenuse of the triangle.

7^2 + x^2 = (36/PI - 2x/PI)^2 – By Pythagoras

.. do some algebra to get ..

-0.594x^2 - 14.6x + 82.3 = 0 – (note: these are rounded here but not for calculating answer)

x = 4.72975 – solving and using the sensible answer for x :p (other answer is negative)

r = (18 - 4.72975) / PI – substituting into earlier equation
= 4.22405 rounded to 5 d. p.

Is "honours" something you do at high school? or where?

EDIT: Just realised radius of 3.5 doesn't make sense based on the problem… :blushing: sorry!
EDIT2: Fixed. Some errors in my algebra :)

honors is just the normal highschool class, but a little more intence(students actually care about the subject, want to be challenged).

Oh, that's cool :) I did a year ahead in maths in high school also.. Finally got a sensible answer after making some silly mistake in the algebra twice -_- I'll edit my post above. It's the same as bolshak, r = 4.22405

I was also ahead a year, I havent took the class in two years :p