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IrinaVladis [17]
3 years ago
14

X and Y are center of circles which intersect at A and C. XA and XC are produced to meet at B and D. Prove AB = CD.

Mathematics
1 answer:
Y_Kistochka [10]3 years ago
3 0

Answer:

On the diagram, construct lines BY, XY and DY.

Now, consider triangles ΔXBY and ΔXDY. We can say that these triangles are congruent by the SAS postulate (they share side XY, XY bisects ∠BYD so ∠BYX=∠DYX, and BY=DY=radius). If they're congruent, their sides are the same so BX=DX.

BX=DX

AB+radius = CD +radius

AB=CD

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When I saw this, I said to myself  "Self !  We don't know anything about
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This just goes to show how stupid I can be when I don't take a little time
to THINK before I go running around screaming.

-- When you draw all the lines from the center to the vertices of the
decagon, you'll have 10 little triangles.

-- The area of the whole thing is 161 square inches, so the area of each
little triangle is 1/10 of that . . . . . <em>16.1 square inches</em>.

-- The area of each little triangle is  (1/2) (base) (height), just like
every other triangle.
The base is the 4.6 inches of one side of the decagon.
              
                                                  Area = (1/2) (base) (height)

Multiply each side by 2:         2 x area = (base) x (height)

Divide each side by (base):  (2 x area) / (base) = height

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Let that be a lesson to both of us.
THINK before you jump.


6 0
4 years ago
Marisol is trying to decide which job to take. She is offered three jobs. The store manager has a salary of $32,500. The
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Hunter-Best [27]
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