Find the area of the pentagon #geometryskills #mathpuzzles #importantgeometryskillsexplained

Find the area of the pentagon #geometryskills #mathpuzzles #importantgeometryskillsexplained

This will be so much appreciated.

grayyeonmath
Important Geometry skills explained
Rectangles
circles
Right Triangle
similarity of triangles
ratio and proportion
ratio
geometry
Find the length X
quadratic equations
completing the squares,quadratic equations
algebra
maths
line segment
midsegment theorem
brian mclogan
area
find the length
satmath
midpoint
length
width
triangles
similar triangles
math
igko
pythagorean theorem problem solving,
pythagorean theorem word problems,
right triangles
mathematics
gre
premath
ixl
prmo

#grayyeonmath
#ImportantGeometryskillsexplained
#rectangles
#circles
#righttriangles
#similarityoftriangles
#triangles
#ratioandproportion
#proportional
#ratio
#geometryskills
#Findthelength
#quadraticequations
completing the squares,
#quadraticequation
#equations
#algebra,
#mathpuzzles
#maths
#linesegment
#midsegmenttheorem
#brianmclogan
#area
#findthelength
#trigonometricratios
#mathpuzzles
#midpoint
#length
#width
#triangles
#similartriangles
#triangles
#math
#igko
#pythagoreantheoremproblem solving,
#pythagorean theorem word problems,
#righttriangles
#triangles
#mathematics
#green
#premath
#satmath
#ixl
#prmo

[jimlocke]

At about 1:15, the arc is tangent to CD but tangency has not been proved. To prove tangency, construct a circle of radius y centered at C and another circle, of radius x centered at D. The centers are 1 apart, the length of CD. The circles can only intersect at one point because their radii add up to 1 and their centers are 1 apart, the intersection being on the line connecting the centers. If the centers were less than 1 apart, they would intersect in two places and if greater they would not intersect. Now construct CF tangent to the arc of radius 1 and DG tangent to the same arc. By exterior angle theorem, CF = y and DG = x. So, F is on a circle of radius y centered at C and G is on a circle of radius x centered at D. There is only one point where the x + y = 1 criteria is satisfied. So, F and G are the same point, but only when x + y = 1.

[RAG]

I agree with jimlocke. It is not at all obvious that the circle is a tangent to CD. This should have been the place for some explanation that was completely lacking.

[vierinkivi]

Annettujen ehtojen puitteissa: Kulma A = 90, y=0. Kuvio on silloin neliö 1X1

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