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WINSTONCH [101]
2 years ago
6

Let O and H be the circumcenter and orthocenter of triangle ABC, respectively. Let a, b, and c denote the side lengths, and let

R denote the circumradius. Find OH^2 if R = 7 and a^2 + b^2 + c^2 = 29.
Mathematics
1 answer:
vovikov84 [41]2 years ago
3 0

Answer:

OH²=412

Step-by-step explanation:

A Circumcenter of a triangle is the point where the three perpendicular bisectors of a triangle meet.

The Orthocenter is the point where all three altitudes of the triangle intersect.

Given any triangle, the orthocenter, circumcenter and centroid are collinear on the Euler line. By Euler's Identity, the distance between the circumcenter and the orthocenter of a triangle is related to the circumradius(R) and the sides(a,b,c) of the triangle by the relation

OH²=9R²-(a²+b²+c²)

R=7, a²+b²+c²=29

OH²=9(7)²-29

OH²=412

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Find the area a of the triangle whose sides have the given lengths. a = 20, b = 15, c = 25 a =?
PIT_PIT [208]

The area of a triangle with sides a = 20, b = 15, and c = 25 is 150.

The sides of the triangle are given as a = 20, b = 15, and c = 25.

We will use Hero's formula to find the area of this triangle.

<h3>What is Heron's formula?</h3>

It is a three-face polygon that consists of three edges and three vertices.

We use Heron's formula to find the area of a triangle with 3 sides:

Herons formula:

Area of a triangle =  \sqrt{s(s-a)(s-b)(s-c)}\\

Where a, b, and c are sides of a triangle.

And s = semi perimeter of a triangle.

s = \frac{a+b+c}{2}

If the sum of two sides of a triangle is greater than the third side of a triangle then the sides of a triangle are true.

Let the given sides be:

a = 20, b = 15 and c = 25.

(20 + 15) > 25

(20 + 25) > 15

(15 + 25) > 20 so the given sides are true.

Now,

Semi perimeter of the triangle:

s = (a+b+c) / 2

s = (20+15+25) / 2

s = 60 / 2

s = 30

Putting s = 30 in the area of the triangle.

we get,

Area of the triangle = \sqrt{s(s-a)(s-b)(s-c)}\\

Area of the triangle = \sqrt{30(30-20)(30-15)(30-25)}\\\\\sqrt{30\times10\times15\times5}\\\\\sqrt{22500}\\\\150

Thus, the area of a triangle is 150.

Learn more about the Area of triangles here:

brainly.com/question/11952845

#SPJ1

3 0
1 year ago
Simplify. Express your answer as a single fraction in simplest form.<br> x x<br> 5
lbvjy [14]

Answer:

\frac{x}{20}

Step-by-step explanation:

Given

\frac{x}{4} - \frac{x}{5}

The LCM of 4 and 5 is 20

= \frac{5x-4x}{20}

= \frac{x}{20}

5 0
2 years ago
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