# MO circles

Juro built the ABCD square with a 12 cm side. In this square, he scattered a quarter circle that had a center at point B passing through point A and a semicircle l that had a center at the center of the BC side and passed point B. He would still build a circle that would lie inside the square and touch the quarter circle k, semicircle l and side AB. Find the radius of such circle.

Result

r =  3 cm

#### Solution:

$|SO| = |SL| + |LO| = R + 6 \ \\ |SB| = |BK | - |KS| = 12 - r \ \\ |OE| = |OB| - |BE| = 6 - r \ \\ \ \\ |SE|² = |SO|² - |OE|² = |SB|² - |BE|² \ \\ (6 + r)² - (6 - r)² = (12 - r)² - r² \ \\ 12r + 12r = 144 - 24r \ \\ 48r = 144 \ \\ r = 144/48 = 3 = 3 \ \text{ cm }$

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
Pythagorean theorem is the base for the right triangle calculator.

## Next similar math problems:

1. Quatrefoil
Calculate area of the quatrefoil which is inscribed in a square with side 6 cm.
2. Pipeline
How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter?
3. Mrak - cloud
It is given segment AB of length 12 cm, where one side of the square MRAK laid on it. MRAK's side length 2 cm shown. MRAK gradually flips along the line segment AB the point R leaves a paper trail. Draw the whole track of point R until square can do the.
4. Circle's chords
In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.
5. 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?
6. Tetrahedron
Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
7. Blocks
There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
8. Three workshops
There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
9. AP - simple
Determine the first nine elements of sequence if a10 = -1 and d = 4
10. Teams
How many ways can divide 16 players into two teams of 8 member?
11. Trigonometry
Is true equality? ?
12. Confectionery
The village markets have 5 kinds of sweets, one weighs 31 grams. How many different ways a customer can buy 1.519 kg sweets.
13. PIN - codes
How many five-digit PIN - code can we create using the even numbers?