MHB How do you calculate the area and arc length of region ABCD using given values?

jevanuD
Messages
11
Reaction score
0

Attachments

  • Sector Question.JPG
    Sector Question.JPG
    19.2 KB · Views: 145
Mathematics news on Phys.org
area of region ABCD ...

$A = \dfrac{\theta}{2}\left(R^2-r^2\right)$

you have $R = 3k$, $r=2k$, and $\theta = \dfrac{3}{4}$

... proceed to solve for $k$

also, arc length difference is $\Delta s = \theta(R - r)$
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Back
Top