You need to remember the Intersecting chords theorem, which states that the products of the lengths of their segments are equal.
You can observe that the diameter is peperndicular to the chord. This divides the chord into two equal segments.
Therefore, based on this and knowing the theorem mentioned before, you can write the following expression:
Finally, you must solve for "x". So you get this result:
2nd figure counting from left side
a chord in geometry cuts a portion of a circle as is shown on the image.
A chord is a straight line segment whose endpoints both lie on the circle
In mathematics, the Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It is expressed as:
c^2 = a^2 + b^2
where c represents the hypotenuse of the right triangle.
We calculate as follows:
16^2 = a^2 + 9^2
a = 5√7
Let the center of the circle be point O.
A right-angled triangle can be drawn using one side of chord X as the base and its height up to point O.
The height of the triangle will be 4 - 2 = 2, and the hypotenuse is the radius of the circle, which is 4.
By Pythagoras' Theorem, 2^2 + (X/2)^2 = 4^2.
So (X/2)^2 = 14, and X = 2√14.
the 2nd on from the left
the 2nd one