The chord of the circle is 6√2 dm and contracts the arc at 90 degrees. Find the circumference and arc length.
| July 23, 2021 | education
The chord AB contracts the arc at 90, then the chord AB is the side of the square inscribed in the circle.
From a right-angled isosceles triangle, in which the angle AOB = BOA = 45, we define the leg AO, which is the radius of the circle.
AO = AB * Sin450 = 6 * √ 2 * √ 2/2 = 6 cm.
Determine the length of the circle.
L = 2 * n * AO = n * 2 * 6 = 12 * n.
Since the arc subtends angle 90, its length is equal to a quarter of the circumference (90/360).
Arc AB = L / 4 = 12 * p / 4 = 3 * p.
Answer: The circumference is 12 * p, the length of the arc is 3 * p.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
