Dragan

As someone put it:

" An error does not become a mistake until you refuse to correct it. "  

In a right triangle, one of the legs is 5 cm smaller than the hypotenuse, and the other leg is 10 cm smaller than the hypotenuse. Find the length of the hypotenuse

(x+5)²+(x+10)²=(x+15)²

Step 1: Simplify both sides of the equation.

2x²+30x+125=x²+30x+225

Step 2: Subtract x² from both sides.

2x²+30x+125−x²=x²+30x+225−x²

x²+30x+125=30x+225

Step 3: Subtract 30x from both sides.

x²+30x+125−30x=30x+225−30x

x²+125=225

Step 4: Subtract 125 from both sides.

x²+125−125=225−125

x²=100

x = 10

sqrt [(10+5)² + (10+10)²] = 25 cm  

tan(80º) = 5.67128181961771   

∠GOR = 100º     consequently    ∠GFR = 50º       ( ∠GFR = ∠GFP )

∠FOQ = 28º       consequently     ∠FGQ = 14º       ( ∠FGQ = ∠FGP )

(∠GFP) + (∠FGP) = ∠RPG  = 64º    

In trapezoid WXYZ, line XY is parallel to line WZ, angle WXZ=105, angle W=43, and angle Y=141. Find YXZ, in degree.

For some reason, I misunderstood this question.

The correct answer is::::              angle YXZ = 32º 

???   Correct your answer. 

1. trapezoid ABCD is inscribed in a semicircle, as shown below. the length of base CD is 7, and the lengths of legs AD and BC are 3. Find the radius of the smicircle.

Radius is  4.5 units     

Two circles intersect at A and B. A common external tangent is tangent to the circles at T and U as shown. Let M be the intersection of line AB and TU. If AB = 9 and  BM = 3 find  TU.

First  case:  both radii are identical:  r = 7.5

                                                         TU = 12 

Second  case:  radii  are different:    r₁ = 5     r₂ =  13.094

The result is the same:                      TU = 12       

You're welcome! 

This is very simple:

If 500 litres of oil was pumped from tank A into tank C, then 650 liters of oil was pumped from tank B into tank C.

Now, there's 1150 liters of oil in tank C

Therefore, using the original amount of oil in tank A, we have:      n = 1150 + 500 = 1650 liters