jugoslav

Angle EFD = 180 - [1/2(180-69) + 1/2(180-78)]

Angle A = 60 degrees

A parallelogram ABCD has a perimeter equal to 124. Let E be the foot of the perpendicular from A to BC, and let F be the foot of the perpendicular from A to CD. If AE= 7 and AF=20, what is the area of the parallelogram?

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AB = x         AD = 62 - x          AE = 7          AF = 20

Triangles ABE and ADF are similar.

x / 7 = (62 - x) / 20

[ABCD] = AE * AD

In triangle ABC, AB =10 and AC =17. Let D be the foot of the perpendicular from A to BC. If BD:CD = 2:5, then find AD.

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BC = x

BD = 2/7x

CD = 5/7x

sqrt[10² - (2/7x)²] = sqrt[17² - (5/7x)²]

x = 21

BD = 2/7 * 21 = 6

CD = 5/7 * 21 = 15

AD = sqrt(AB² - BD²) = 8

Wrong question

Instead of 2:3 MUST BE 2:5 

Arc LPM = 360º - 72º   

Let me turn this not-so-smart question into an interesting one:

Points L and M lie on a circle centered at O, and the measure of arc LM on this circle is 72 degrees.  The circle passing through points O, L, and M is drawn.  Find the measure of arc LOM on the larger circle, in degrees.

Let me correct this question:

Let X, Y, and Z be points such that XZ/ZY = ZY/XY = 2/3. If Y = (1, 7), Z = (-1, -9), then what is the sum of the coordinates of X?

ZY = √20

XZ = 1/2(ZY = √5

XY = 2(ZY) = √80

Such a triangle is NOT possible!!!

ZY + XZ MUST BE greater than XY!!!

Points A(0,0), B(9,6) and C(6,12) are vertices of triangle ABC. Point D is on segment AB such that 3(AD) = DB, point E is on segment BC such that 3(BE) = EC, and point F is on segment CA such that 4(CF) = FA. What is the ratio of the area of triangle DEF to the area of triangle ABC? Express your answer as a common fraction.

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Using the shoelace method we find that [ABC] = 36, and [DEF] = 16.65.

[DEF] / [ABC] = 37 / 80

Height of a cylinder = y

Height of a cone = 27y