# RT and circles

Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.

Result

a =  37.83
b =  26.17
c =  46

#### Solution:

$R = \dfrac{c}{2} \ \\ c = 2 R = 46 \ \\ \ \\ r = \dfrac{ a+b-c}{2} \ \\ a + b = 64 \ \\ a^2 + b^2 = 2116 \ \\ \ \\ 2a^2 -128a +1980 =0 \ \\ \ \\ p=2; q=-128; r=1980 \ \\ D = q^2 - 4pr = 128^2 - 4\cdot 2 \cdot 1980 = 544 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ 128 \pm \sqrt{ 544 } }{ 4 } = \dfrac{ 128 \pm 4 \sqrt{ 34 } }{ 4 } \ \\ a_{1,2} = 32 \pm 5.83095189485 \ \\ a_{1} = 37.8309518948 \ \\ a_{2} = 26.1690481052 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 2 (a -37.8309518948) (a -26.1690481052) = 0 \ \\$
$b=(-(-128) - (23.3238075794))/ (2 \cdot \ (2))=26.17$
$c=2 \cdot \ 23=46$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.

## Next similar math problems:

1. Chord - TS v2
The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
2. Chord BC
A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]?
3. Solve 3
Solve quadratic equation: (6n+1) (4n-1) = 3n2
4. Catheti
The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
5. ABS CN
Calculate the absolute value of complex number -15-29i.
6. Vector 7
Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
7. Euclid2
In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
8. RTriangle 17
The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs.
9. Circle chord
Determine the radius of the circle in which the chord 6 cm away from the center of the circle is 12 cm longer than the radius of the circle.
Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
11. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
12. Equation
Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
13. Discriminant
Determine the discriminant of the equation: ?
14. Roots
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?