In a circle with a diameter of 50 cm, a chord is drawn 10cm from the origin. How long is the chord?
Draw a diagram.
Let the center of the circle be O
Let the chord intersect the circle at A,B
Draw a radius OC ⊥ AB, intersecting it at D.
Now you have a right triangle ODB such that
OB = 25
OD = 10
half the chord is DB^2 = 25^2 - 10^2
...
To find the length of a chord in a circle, we need to use the Pythagorean theorem.
Let's label the center of the circle as point O, the origin where the chord is drawn as point A, and the point where the chord meets the circumference as point B.
Given that the diameter of the circle is 50 cm, we can determine that the radius (OB) is half of the diameter, which is 50/2 = 25 cm.
Since the chord is drawn 10 cm from the origin, this means that the distance from A to O is 10 cm.
We can now apply the Pythagorean theorem to find the length of the chord AB. According to the theorem, the square of the hypotenuse (AB) is equal to the sum of the squares of the other two sides. In this case, AB is the hypotenuse.
Using the Pythagorean theorem:
AB^2 = AO^2 + OB^2
AB^2 = 10^2 + 25^2
AB^2 = 100 + 625
AB^2 = 725
Taking the square root of both sides:
AB ≈ √725
AB ≈ 26.93 cm
Therefore, the length of the chord AB is approximately 26.93 cm.