Dragan

Triangles PQA and CRD are similar!!!

AQ / AP = DR / DC

1 / 2 = DR / 5

DR = 5/2

Tesla would agree with both, Jugoslav and Alan because their answers are correct!!! 

Hi, cryptoaops!

That diagram is ok, but my answer "Area of a triangle QRP = 3√3" is NOT correct!!!

Link:  https://web2.0calc.com/questions/geometry_49612

The correct answer is   [QRP] = 5.569219381 square units!!! 

Link:   https://web2.0calc.com/questions/quick-hard-question-help-asap

(I don't know how to convert that decimal into radical.)

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or space by the same distance in a given direction.

A rotation is a transformation that turns a figure about a fixed point called the center of rotation.
• An object and its rotation are the same shape and size, but the figures may be turned in different directions.
• Rotations may be clockwise or counterclockwise.

I made a mistake!!! I used the wrong angle.

Instead of √2 and √8  should be  1 and 3

Phill's answer is correct!!!

Please don't trust me. I'm not Nikola Tesla.

In the coordinate plane, A = (0,0), B = (0,4), and C = (5,0).  If P is a point inside triangle ABC such that AP = sqrt(10) and BP = 3*sqrt(2), then find CP.

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Use the law of cosines to find ∠BAP.    Find ∠PAC

Using ∠PAC and line AP, calculate line segments AD and PD

CP = sqrt[PD² + (AC - √8)²]     ==>   CP ≈ 2.591 

a + b = 4 + (√40)/2

∠BAO = sin^-1(3.5 / 5) = 44.427 deg.

BO = 2.5 / cos(∠BAO) = 3.50070021

OM = sqrt(BO² - BM²) = 0.070014           ( M is the midpoint on BC)

Area OBC = BM * OM = 0.245049744 units squared

Question: If the area of triangle ABC is 27, what is the value of p?

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In my above post, I was using the wrong diagram. 

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Answer:      A (3, 12)         B (12, 0)           C (0, p)

1/   AB = arctan(12 / 9) = 15

2/   CY = 2*27 / 15 = 3.6

3/    ∠ABO  ≅  ∠YCZ = arctan(12 / 9) = 53.13010235º

4/   OZ = 12 * tan ∠ABO = 16

5/   CZ = CY / cos∠YCZ = 6

6/   p = OZ - CZ = 10

( See above diagram ) 

If the area of triangle ABC is 27, what is the value of p?

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Solving this geometry problem in several easy steps:

1)   AB = sqrt(12² + 10²) = 15.62049935

2)   CY = 2*27 / AB = 3.456995759

3)   ∠ABO ≅ ∠ YCZ = arctan(12 / 10) = 50.19442891º

4)   OZ = 12 * tan∠ABO = 14.4

5)   CZ = CY / cos∠YCZ = 5.4

6)   p = OZ - CZ = 9