Isosceles triangle has , and a circle with radius is tangent to line at and to line at . What is the area of the circle that passes through vertices , , and
Answers
The circle that passes through the vertices of triangle ΔABC (A, B, C) is the
circumscribing circle of triangle ΔABC.
The area of the circle that passes through vertices A, B, and C, is (C) 26·π
Reasons:
The given parameters are;
Side length of isosceles triangle ΔABC; [tex]\overline{AB}[/tex] = [tex]\overline{AC}[/tex] = 3·√6
Radius of circle tangent to [tex]\overline{AB}[/tex] at B and [tex]\overline{AC}[/tex] at C = 5·√2
Required:
Area of the circle that passes through vertices A, B, and C
Solution:
Angle ∠BAO is given as follows;
[tex]\angle BAO = arctan\left(\dfrac{5 \cdot \sqrt{2} }{3 \cdot \sqrt{6}} \right) = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]
Therefore;
[tex]\angle BOA = 90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]
[tex]\overline{BC} = 2 \times 5 \cdot \sqrt{2} \times sin\left(90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right) = 15\cdot \sqrt{\dfrac{6}{13} }[/tex]
∠ABO' = ∠BAO' (Base angles of isosceles triangle ΔABO')
[tex]\angle BAO' = \angle BAO = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]
Therefore;
[tex]\angle BO'A = 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]
From sine rule, we have;
[tex]\dfrac{\overline{AB}}{sin \left(\angle BO'A \right)} = \mathbf{\dfrac{\overline{BO'}}{sin \left(\angle BAO' \right) \right)}}[/tex]
Which gives;
[tex]\mathbf{\dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)}} = \dfrac{\overline{BO'}}{sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right)}[/tex]
Using a graphing calculator, we get;
[tex]\overline{BO'} = \dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)} \times sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right) = \sqrt{26}[/tex]
The radius of the circumscribing circle [tex]\overline{BO'}[/tex] = √(26)
Therefore, area of the circumscribing circle, [tex]A_{O'}[/tex] = π·(√(26))² = 26·π
The area of the circle that passes through vertices A, B, and C, is (C) 26·π
Learn more here:
https://brainly.com/question/17147358
The possible question options obtained from a similar question online are;
(A) 24·π (B) 25·π (C) 26·π (D) 27·π (E) 28·π
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Answers
Answer:
AC ≈ 50.5
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan29° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{28}{x}[/tex] ( multiply both sides by x )
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Answer:
50.5
Step-by-step explanation:
In the right triangle, focus on angle A. The side marked 28 is the opposite side, and the side marked x is the adjacent side. The trigonometric ratio that uses those two side is the tangent ratio.
tangent = (opposite) / (adjacent)
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Answers
Answer:
5%
Step-by-step explanation:
First let's find the interest,
$ 115.50 - $ 110
= $ 5.5
Now let's use this formula to find the simple percent interest.
Simple interest = P × r × t / 100
Here,
P = Principle
r = rate
t = time
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Therefore, the percentage is 5%
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Answers
Answer: 72.5%
Step-by-step explanation:
I used trial and error to figure this out.
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Reformatting the input:
Changes made to your input should not affect the solution:
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STEP 1:
Equation at the end of step 1
6
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10
STEP 2:
3
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5
Equation at the end of step 2:
3
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STEP 3:
Equation at the end of step 3
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Answer:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Answers
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
a fraction in which the numerator is greater than the denominator, such as 5/4.
Step-by-step explanation:
A fraction consists of a Numerator and a Denominator. The numerator tells how many parts out of all are there. The denominator tells how many total parts are there. A fraction in which the numerator is greater than the denominator is called an improper fraction.
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
24
Step-by-step explanation:
x-3=5, solve for x so that x=5+3
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Suppose an annuity pays 7.0% annual interest, compounded annually. If you invest $3,000 every year for 5 years, what percentage of the balance in the account is interest earned?
Round your answer to the nearest hundredth of a percent.
Answers
Answer:
13.05%
Step-by-step explanation:
The value of an ordinary annuity earning interest compounded annually is ...
A = P((1 +r)^n -1)/r . . . . . interest rate r for n years on principal payments P
For this account, the balance after 5 years will be ...
A = 3000((1 +.07)^5 -1)/0.07 = 3000·5.750739
The sum of payments is ...
payment total = 3000·5
Then the amount of interest is ...
3000·(5.750739 -5) = 3000·0.750739
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(3000·0.750739)/(3000·5.750739) × 100% ≈ 13.05%
About 13.05% of the balance is interest earned.
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A
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Answer:
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Write the prime factorization of 185.
Answers
Answer:
5 ⋅ 37
Step-by-step explanation:
185 has factors of 5 and 37.
Answer:
Step-by-step explanation:
All Factors of 185: 1, 5, 37 and 185.
Negative Factors of 185: -1, -5, -37 and -185.
Prime Factors of 185: 5, 37.
Prime Factorization of 185: 5^1× 37^1
Sum of Factors of 185: 228.
Jenna's basketball team is behind by eleven points. If their team makes a three-point shot, they will need to score
another
polnts to tie the game.
zero
fourteen
eight
eleven
Answers
Answer:
8
Step-by-step explanation:
11-3=8
11-3=8 must subtract for anser