1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kondaur [170]
3 years ago
10

A circle passes through points A(7,4), B(10,6), C(12,3). Show that AC must be the diameter of the circle.

Mathematics
1 answer:
Artist 52 [7]3 years ago
6 0

so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.

in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{12}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{12+7}{2}~~,~~\cfrac{3+4}{2} \right)\implies \left( \cfrac{19}{2}~~,~~\cfrac{7}{2} \right)=M\impliedby \textit{center of the circle}

now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}}) \\\\\\ BM=\sqrt{\left( \frac{19}{2}-10 \right)^2+\left( \frac{7}{2}-6 \right)^2} \\\\\\ BM=\sqrt{\left( -\frac{1}{2}\right)^2+\left( -\frac{5}{2} \right)^2}\implies \boxed{BM\approx 2.549509756796392}

You might be interested in
If u make 120.45 in 15 2/3 hours how long did u work if u made 40.15 ?
Novosadov [1.4K]

Answer:

about 5.22hrs

Step-by-step explanation:

cross multiply

<u>120.45</u>          <u>?</u>

15.67         40.15

120.45*40.15

=629.1505

629.1505/15.67

=5.2233333...

5 0
3 years ago
Need the answers for 4-8
Fed [463]

Answer:

hope this helps you out ask me if you need more help

6 0
3 years ago
The base of the pyramid is a square what is the surface area if the pyramids height is 4 feet in the area of the base is 36 ft.?
KATRIN_1 [288]

Answer:

96 ft²

Step-by-step explanation:

The general formula for the surface area of a pyramid is:  

SA = \frac{1}{2}pl + B, were p = the perimeter of the base, l = the slant height and B = the area of the base

Since the area of the base is 36 ft², then each side is √36, or 6 ft. The perimeter is the sum of all the sides, so 6 x 4 = 24 ft.

Given the overall height of the pyramid is 4 feet, you can use the Pythagorean Theorem (a² + b² = c²) to find the slant height (hypotenuse) of the pyramid.  Using 3 feet for 'a' and 4 feet for 'b':

3² + 4² = c² or 9 + 16 = 25

25 = c² or c = 5

SA =  \frac{1}{2}(24)(5) + 36

SA = 60 + 36 = 96 ft²

8 0
3 years ago
What is the area cause I am having a hard trouble
fomenos
The figure consists of a triangle and two rectangles.

-----------------------------
Top Triangle:
-----------------------------
Height = 22 - 10 - 7 = 5cm
Base = 20 - 5 - 5 - 10cm
Area of triangle = 1/2 x 5 x 10 = 25 cm²

-----------------------------
Middle Rectangle:
-----------------------------
Length = 10cm
Width = 7cm
Area = 10 x 7 = 70 cm²

-----------------------------
Bottom Rectangle:
-----------------------------
Length = 20 cm
Width = 10 cm
Area = 20 x 10 = 200 cm²

-----------------------------
Total Area:
-----------------------------
Area = 25 + 70 + 200 = 295 cm²

-----------------------------
Answer: Area = 295 cm²
-----------------------------

6 0
3 years ago
Suppose a class of 50 students has 20 males and 30 females. The insturctor will pick 1 (different) student to compete in 3 diffe
Pie

Answer:

Step-by-step explanation:

Total = 50

Males = 20

Females = 30

a) P(exactly 1 female) = P(1 female , 2 male)

(30C1 * 20C2) / (50C3) = 30*190/19,600 = 0.2908

b) P(at least 2 males) = 1 - (P(0 males) + P(1 males))

= 1 - 30C3 * 20C0/50C3 - 30C2 * 20C1/50C3

= 1 - 4060*1/19,600 - 435*20/19,600 = 6840/19600 = 0.3489

4 0
3 years ago
Read 2 more answers
Other questions:
  • The circumference of a circle varies directly with its radius. if the circumference of a circle with a radius of 1.5 inches is 9
    13·2 answers
  • I NEED HELP ASAP QUESTION ON IT NOW
    11·1 answer
  • What is the value for ƒ(x) = 4^2x - 100 when x = 2 ?
    8·1 answer
  • Please help due today!
    6·1 answer
  • A statistics practitioner determined that the mean and standard deviation of a data set were 120 and 30, is respectively. What c
    10·1 answer
  • What mathematical relationship between variables is suggested by a graph showing a diagonal line from the lower left to the uppe
    12·2 answers
  • Solve the system algebraically. y = 3 - x 3x + 4y = 1 What is the value of x? -11 17/2 11
    7·2 answers
  • What is the following sale price for a phone charger with an original price of $1.99 after applying a discount of 20%
    11·1 answer
  • Share 56 sweets in the ratio 2 : 5.
    10·1 answer
  • Find the rate of change of the linear function shown in the graph. Then find the initial value.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!