A Very Nice Geometry Problem From China | 2 Different Methods

GET MY EBOOKS
•••••••••••••••••••••••
150 Challenging Puzzles with Solutions : payhip.com/b/y...
Function : payhip.com/b/y...
Sequence and Series : payhip.com/b/B...
Differentiation : payhip.com/b/W...
Indefinite Integration : payhip.com/b/8...
Definite Integration + Area under the Curve : payhip.com/b/1...
Trigonometry : payhip.com/b/8...
OTHER CHAPTERS : COMING SOON.....
--------------------------------------------------------------------------------
Join the channel to become a member
/ @mathbooster

[@marioalb9726]

tanα = 2/5 --> α=21,8014° b = 5+2 = 7 cm x = c - 5 = b/cos2α - 5 = 14/3 cm A = A₁-A₂ = 5.x - πR² = 70/3-4π A = 10,767 cm² (Solved √)

[@marioalb9726]

tanα = 2/5 --> α=21,8014° b = 5+2 = 7 cm h = b tan2α = 20/3 cm A = ½bh - πR² = ½ 7 20/3 - π2² = 70/3-4π A = 10,767 cm² (Solved √)

[@jimlocke9320]

Using the designations give at 0:45, construct OC and OP. Note that ΔOPC and ΔOSC are congruent by side-side-side. Therefore

[@devondevon4366]

70/3 - 4pi or 10.767 7^2 + ( n + 2)^2 = (n+5)^2 49 + n^2 + 4 + 4n =n^2 + 10n + 25 28 = 6n 14/3 = n bases of triangle are (14/3 + 2 ) and 7 or 20/3 and 7 Area of triangle is 10/3 *7 = 70/3 or 23.333 Area of circle = 2^2 pi or 4pi Hence, shaded area = 70/3 - 4pi or 10.767

[@michaeldoerr5810]

The shaded area is 70/3-4pi units square. I have noticed that the second method makes use of the same circle method as before and uses the semiperimeter. How many problems that you know require BOTH that circle theorem and the semiperimeter???

[@prossvay8744]

Shaded area =1/2(20/3)(7)-4π=70/3-4π.❤

[@WahranRai]

Math Booster you must be rigorous You call S a vertex of the square and then S as semi-perimeter In EUROPE and in the rest of the world, the radius is R or r (gamma design angle in triangle in general)

[@Grizzly01-vr4pn]

Kind of valid first point, although it's impossible to tell if he's using 'S' for one and 's' for the other. For your second point, he is actually writing 'r' believe it or not, it's just that his appalling handwriting makes it look like a lower-case gamma. Very annoying to see.

[@himo3485]

(2+5)²+(2+x)²=(x+5)² 49+4+4x+x²=x²+10x+25 6x=28 x=14/3 2+14/3=6/3+14/3=20/3 Shaded area = 20/3*7*1/2 - 2*2*π = 70/3 - 4π

[@giuseppemalaguti435]

(2+x)^2+7^2=(5+x)^2..4x+53=10x+25..x=28/6=14/3...Ared=(2+14/3)7/2-4π=20*7/6-4π=70/3-4π

[@sorourhashemi3249]

Thanks. Easy

[@RealQinnMalloryu4]

(2)^2=4A/ (5)^2=25O/ {4A/+25O/}=29AO/ 180°ABC/29AO=6.6ABCAO/3^2.3^2 1^1.3^2 (AO/ABC ➖ 3AO/ABC+2).

[@imetroangola4943]

This math, my friend, doesn't exist! What planet are you from? Are you a UFO by any chance?