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:

Solution in text r =

Try another example






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

Showing 0 comments:
1st comment
Be the first to comment!
avatar




To solve this verbal math problem are needed these knowledge from mathematics:

Pythagorean theorem is the base for the right triangle calculator.

Next similar math problems:

  1. Quatrefoil
    4listek Calculate area of the quatrefoil which is inscribed in a square with side 6 cm.
  2. Tree trunk
    circle_and_square What is the smallest diameter of a tree trunk that we can cut a square-section square with a side length of 20 cm?
  3. Mrak - cloud
    otaceni_ctverce 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
    twochords 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. Chords
    chords How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
  6. Theorem prove
    thales_1 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?
  7. Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
  8. Teams
    football_team How many ways can divide 16 players into two teams of 8 member?
  9. Legs
    rak Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
  10. Three workshops
    workers_24 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?
  11. Sequence
    seq_1 Write the first 6 members of these sequence: a1 = 5 a2 = 7 an+2 = an+1 +2 an
  12. Sequence 2
    seq2 Write the first 5 members of an arithmetic sequence a11=-14, d=-1
  13. Sequence
    a_sequence Write the first 7 members of an arithmetic sequence: a1=-3, d=6.
  14. Examination
    examination The class is 21 students. How many ways can choose two to examination?
  15. Blocks
    cubes3_1 There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
  16. PIN - codes
    pin How many five-digit PIN - code can we create using the even numbers?
  17. Confectionery
    cukrovinky The village markets have 5 kinds of sweets, one weighs 31 grams. How many different ways a customer can buy 1.519 kg sweets.