jugoslav

Triangles BDC and ACD are coplanar and isosceles. If we have angle ABC = 70, what is angle BAC, in degrees?

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The diagram shows that the angle ABC cannot be 70º; the max is 44º (as integer)

angle B = 168 degrees

Angle AHB = 106º  

There are two circles of equal radius 1 that are centered at points A and B, respectively, and externally tangent to each other. A tangent DC is drawn to both circles, and a square EFGH fits between the circles such that points G and H lie on the line segment DC.

Find the side length of the square.

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∠DNM = ∠EDM = tan^-1(1/2)

DE = sin∠DNM * DN 

EH = sin∠EDM * DE

The side length of the square, GH = 2/5 units  

PA must be shorter than PT!!!

A, B, and T are three points lying on a circle.  If PT is a tangent line of the circle and AB = 7 and PT = 12, then what is PA?

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PT² = PA * PB         PA => x

144 = x (x + 7)

x² + 7x - 144 = 0

x = 9

The first row should be     x+y = sqrt(9² + 12²) = 15

AQ is a diameter of a circle.

If AP * PQ = 55 then BP * PC = 55      

AB = sqrt(AP² + BP²) = 4√11

In rectangle ABCD, AB = 6 and BC = 4.  EF is parallel to BC, and EC = 1.  Rectangle GHIJ is inscribed in rectangle AFED, such that it is similar to rectangle ABCD.  Find the ratio of the area of GHIJ to the area of ABCD.

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The ratio of the area of GHIJ to the area of ABCD is 36/65

(Don't ask me how I've done it.) 

x+y = sqrt(92 + 122) = 15

z = (9 * 12) / 15  = 7.2

x+y+z = 22.2 units