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
Ksivusya [100]
3 years ago
14

Find the length of the radius of the circle, which is inscribed into a right trapezoid with lengths of bases a and b.

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

Answer:

  r = (ab)/(a+b)

Step-by-step explanation:

Consider the attached sketch. The diagram shows base b at the bottom and base a at the top. The height of the trapezoid must be twice the radius. The point where the slant side of the trapezoid is tangent to the inscribed circle divides that slant side into two parts: lengths (a-r) and (b-r). The sum of these lengths is the length of the slant side, which is the hypotenuse of a right triangle with one leg equal to 2r and the other leg equal to (b-a).

Using the Pythagorean theorem, we can write the relation ...

  ((a-r) +(b-r))^2 = (2r)^2 +(b -a)^2

  a^2 +2ab +b^2 -4r(a+b) +4r^2 = 4r^2 +b^2 -2ab +a^2

  -4r(a+b) = -4ab . . . . . . . . subtract common terms from both sides, also -2ab

  r = ab/(a+b) . . . . . . . . . divide by the coefficient of r

The radius of the inscribed circle in a right trapezoid is r = ab/(a+b).

_____

The graph in the second attachment shows a trapezoid with the radius calculated as above.

You might be interested in
The average of 100 measurements is 23 and the average of 50 additional measurements is 27.
Elden [556K]
Total value of 100 measurements
100 * 23
2300

Total value of additional 50 measurements
50 * 27
1350

Total value of 150 measurements
2300 + 1350
3650

Average of 150 measurements
3650 / 150
24.3

25 > 24.3

Answer is B
8 0
3 years ago
Order from least to greatest
RUDIKE [14]
Do them backwards and you will get the answer
5 0
3 years ago
Read 2 more answers
Jackson rode his bike 2.5 miles from his house to school; how many yards did he ride
djyliett [7]

Answer:

4400 yards

Step-by-step explanation:

Convert miles into yards.

7 0
3 years ago
Simplify: 28a8+14a²<br> Enter the original expression if it cannot be<br> simplified.
Korolek [52]

Answer:

14a^2(2a^6+1)

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
What is an equation in point-slope form of the line that passes through the point (6, −2) and has a slope of 3? A. y + 2 = 3(x −
Nostrana [21]

Answer:

answer A is correct because the formula of equation in point slope is

y-y1=m(x-x1)

where,(x1,y1)point is given that is (6,-2)

slope=m=3

8 0
3 years ago
Other questions:
  • In the figure shown, what is the measure of angle x? (5 points) 115 degrees 130 degrees 145 degrees 150 degrees
    7·1 answer
  • Start at 3 and create a pattern with the rule add 2 what is the 5th rumber in the answer
    11·1 answer
  • Can someone help me I forgot how to do this
    15·1 answer
  • What type of exponential function is f(x)=0.6(2.4)^x ?
    15·2 answers
  • What is 164.362 rounded to 4, 3 and 1 significant figures​
    12·1 answer
  • A website charges $3 for each
    12·2 answers
  • Y=6x . What is the new equation if it's shifted 5 units left
    9·1 answer
  • Find the area of a circle with the circumference 32pi
    5·1 answer
  • A. -2x + y = -2
    10·1 answer
  • Please help on this mathematical problem
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!