Dragan

Sides of an obtuse triangle AB, BC, and AC have midpoints E, F, and D. G is the point of intersection of all 3 medians.

If AB = 7, BC = 9, and BG = 3 then what's the length of AC? (AC is the longest side)

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The Median Theorem states that the medians of a triangle intersect at a point called the centroid that is two-thirds of the distance from the vertices to the midpoint of the opposite sides.

If BG is 3 then BD = 3 * 1.5 = 4.5

Since we have: AB=7,  BC=9, and BD=4.5 we can use  Apollonius's theorem to find AC.

|AB|² + |BC|² = 2( |AD|² + |BD|² )

AC = 2|AD|  ≈ 13.379

A right triangle has legs of length 6 and b and a hypotenuse of length c.The perimeter of the triangle is18.Compute c.

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a = 6               b = 6 / tanA              c = sqrt[6² +(6 / tanA)²]

We'll use this information to calculate the angle A       a + b + c = 18

6 + 6 / tanA + sqrt[6² + (6 / tanA)²] = 18                angle A = 53.13010235º

Side  b = 6 / tanA = 4.5

Side  c = sqrt(a² + b²) = 7.5

Which one's 18, AD, or EG?

Points ABCDEFG form 7 equal arcs.

Arc AB = 360 / 7

Ange AEB = 1/2 (arcAB)

The sum of all 7 angles is 180 degrees. 

Hint:  use a right-angled triangle with legs of 20 and 25

 The length of the shortest leg = [sqrt(16² - 8²)] / 2

Important: If one secant and one tangent are drawn to a circle from one exterior point, then the square of the length of the tangent is equal to the product of the external secant segment and the total length of the secant.

PY² = PB * PA

Here's a link:    https://web2.0calc.com/questions/help_54234

angle CXY = 70º

This diagram may support my answer. If an explanation is needed, I'm willing to provide it.