# Two chords

From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.

Correct result:

t =  6.928 cm

#### Solution:

$D=8 \ \text{cm} \ \\ A=60 \ ^\circ \ \\ B=A/2=60/2=30 \ ^\circ \ \\ r=D/2=8/2=4 \ \text{cm} \ \\ \ \\ r^2=r^2 + t^2 - 2 \cdot \ r \cdot \ t \cdot \ \cos B \ \\ t^2=2 \cdot \ r \cdot \ t \cdot \ \cos B \ \\ t=2 \cdot \ r \cdot \ \cos B ^\circ =2 \cdot \ r \cdot \ \cos 30^\circ \ =2 \cdot \ 4 \cdot \ \cos 30^\circ \ =2 \cdot \ 4 \cdot \ 0.866025=6.928 \ \text{cm}$

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!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Cosine rule uses trigonometric SAS triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Chord of triangle
If the whole chord of the triangle is 14.4 cm long, how do you calculate the shorter and longer part?
• On a line
On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].
Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
• Square and circles
The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a.
• Dodecagon
Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
• Cylinder container
The cylindrical container with a diameter of 1.8 m contains 2,000 liters of water. How high does the water reach?
• Sailboat
The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck.
• In the
In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm2.
• Hexagonal pyramid
Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.
• Coils of transformer
The primary coil of the transformer has 1100 turns and is connected to a voltage of 220V. How many turns does the secondary coil have when the voltage on it is 55 V? Determine the transformation ratio and decide what kind of transformation is it.
• Coils of transformer
The primary coil of the transformer has 400 turns, a current of 1.5 A passes through it and is connected to a voltage of 220 V. For the secondary coil, find the voltage, current, and a number of turns if the transformation ratio k = 0.1.
• Shell area cy
The cylinder has a shell content of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder.
• The cylinder
The cylinder has a surface area of 300 square meters, while the height of the cylinder is 12 m. Calculate the volume of this cylinder.