# Examples for 9th grade - page 42

- Circle tangent

It is given to a circle with the center S and radius 3.5 cm. Distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p. - Chord MN

Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle. - Rectangle and circle

The rectangle ABCD has side lengths a = 40 mm and b = 30 mm and is circumscribed by a circle k. Calculate approximately how many cm is circle long. - Machines 2

2 machines for 50 hours produces 2,000 products. How many machines need to buy to make in 30 hours 15,000 products? - Canister

Gasoline is stored in a cuboid canister having dimensions 44.5 cm, 30 cm, 16 cm. What is the total weight of a full canister when one cubic meter of gasoline weighs 710 kg and the weight of empty canister is 1.5 kg? - Deposit 3

After a year had Martin on bank account € 2028. What was the interest rate when the initial deposit was € 1879? - Clocks

How long track travel the second hand in 46 hours, the end of which is 4 cm long. - Semicircle

To a semicircle with diameter 10 cm inscribe square. What is the length of square sides? - Trees

Loggers wanted to seed more than 700 and less than 800 trees. If they seed in rows of 37, left them 8 trees. If they seed in rows of 43, left the 11 trees. How many trees must seed ? - 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. - Bottle

Bottle with wine costs 58 USD. Wine is 27 USD more expensive than the empty bottle. How much is the bottle itself? - Rectangle

The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to rectangle. - Traffic collision

When investigating a traffic accident, it was found that the driver stopped the vehicle immediately after the accident by constant braking on a 150 m track in 15 seconds. Do you approve that the driver exceeded the permitted speed (50 km/h) in the village. - Rhombus

ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus. - Circular flowerbed

Circular flowerbed with diameter 8 m we split by concentric circle to circle and annulus with the same area. Determine the radius of the circle. - Midpoint of segment

Point A has coordinates [-16; 23] and the midpoint of the segment AB is the point [2; 12]. What are the coordinates of point B? - Rectangular trapezoid

Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC. - Olympics

In how many ways can be placed 6 athletes on the podium at the Olympics? Depend on the color of the metal. - Friends

Some friends had to collect the sum 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends? - Rectangle Anton

Difference between length and width of the rectangle is 8. Length is 3-times larger than the width. Calculate the dimensions of the rectangle.

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