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Rangpur Secondary (Higher Secondary) 2011/10

Posted: Wed Feb 02, 2011 6:50 pm
by Moon
Problem 10:
$ABCD$ is a rectangle where $AB = 3$, $BC = 6$ and $CD=CE$. The area of the part of the quadrangle $CDGF$ that lies outside the circular arc can be expressed as $a-b \sqrt{3}-\frac{c\cdot \pi}{4}$ where $a$, $b$, $c$ are integers. Find $a+b+c$.

Re: Rangpur Secondary 2011/10

Posted: Wed Feb 02, 2011 8:07 pm
by Tahmid Hasan
where is the point $E$ situated?

Re: Rangpur Secondary 2011/10

Posted: Wed Feb 02, 2011 8:53 pm
by Moon
Diagram uploaded. :)

Re: Rangpur Secondary (Higher Secondary) 2011/10

Posted: Thu Feb 03, 2011 12:16 pm
by Mehfuj Zahir
Connect the point C,G.Find the area of triangle CGF=9.SO,BG=6.Then using pythagoreous find BF&get GF.Now the area of triangle CGF&CDG is equal.Find area of quadrangle DGFC.The angleCDF is 30.Then subtract area inscribed by the arch DF from quadrangle DGFC.Ans should be a+b+C=30