civonamzuk

In the diagram below, EU = 8, UF = 7,GV = 5, VH = 16, and UV= 8. Find XY.

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UX => m            VY => n

m(8 + n) = 7 * 8         m = 56 / (8 + n)

n(8 + m) = 5 * 16        

n[8 + 56 / (8 + n)] = 80        n ≈ 6.787

m = 56 / (8 + n)                   m ≈ 3.787

XY = √345   ≈ 18.574

Oops!!!

 Let ABC be a triangle with AB = 13, BC = 14, and AC = 15. The incircle

of ABC touches AB and AC at points D and E, respectively. The triangle’s
A−excircle (tangent to segment BC and the extended rays AB and AC, outside of
the triangle) touches BC at P. Find [ADE]/[BDP].

AX = sqrt(AC² + CX²)

That was easy.

What's the length of CY?

Let angle BAD = 90º

BD = 5

AX = 2.4

BX = 1.8

DX = 3.2

CX = sqrt(CD² - DX²) 

BC = sqrt(BX² + CX²) = √29

BC / CE = AB / AE

Let XY be a tangent to a circle, and let XBA be a secant of the circle, as shown below. If AX = 15 and XY = 8, then what is AB?

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AX = 15         XY = 8         BX = x

x(AX) = (XY)²          x = 4 ⁴/₁₅

AB = AX - x = 10 ¹¹/₁₅   

BC = sqrt(8² - 7²) = √15

DX = sqrt(15 + 1) 

Ricky has some cookies. He ate 1/8 of his cookies and an additional 14 cookies on Friday. He then ate 3/10 of the remaining cookies and an additional 24 cookies on Saturday. He ate 40 cookies on Sunday and had 34 cookies left. How many cookies did Ricky have at first?

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     x - [(1/8x + 14) + 3/10(x - 1/8x - 14) + 24 + 40] = 34

 Total  I     Friday   I        Saturday                 I Sun  I  left

x = 176  

Let triangle ABC have centroid G. D lies on AB such that AD/BD=2/3 and E lie on AC such that AE/CE =4/5. Lines DG and EG intersect BC at points P and Q, respectively. Find PQ/BC.

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I used an equilateral triangle and the answer is: PQ / BC = 7 / 12

Here's my work