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  cm |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 }

Try another example


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...):

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




Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Quatrefoil
    4listek Calculate area of the quatrefoil which is inscribed in a square with side 6 cm.
  2. Pipeline
    pipeline How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter?
  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. 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?
  6. Tetrahedron
    tetrahedron (1) Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
  7. Blocks
    cubes3_1 There are 9 interactive basic building blocks of an organization. How many two-blocks combinations are there?
  8. 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?
  9. AP - simple
    sigma_1 Determine the first nine elements of sequence if a10 = -1 and d = 4
  10. Teams
    football_team How many ways can divide 16 players into two teams of 8 member?
  11. Trigonometry
    sinus Is true equality? ?
  12. 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.
  13. PIN - codes
    pin How many five-digit PIN - code can we create using the even numbers?
  14. Add vector
    vectors_2 Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
  15. Sequence
    seq_1 Write the first 6 members of these sequence: a1 = 5 a2 = 7 an+2 = an+1 +2 an
  16. 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?
  17. Reference angle
    anglemeter Find the reference angle of each angle: