Question

Line segments MP and ML are perpendicular chords in circle O. MP = 10 and ML = 24.

Which statements about circle O are true? Check all that apply.

-The radius of circle O is 13.
-The diameter of circle O is 34.
-LP is a diameter of circle O.
-∠LMP intercepts a semicircle.
-The measure of arc LP is 90°.

Answer 1

The diameter of this circle at the same time hypotenuse of triangle LMP
|LM|²=24²+10²
|LM|=√(676)=26 - diameter
so radius =26/3=13
-The radius of circle O is 13.
-LP is a diameter of circle O.
-∠LMP intercepts a semicircle.

Answer 2

The Pythagoras' Theorem in mathematics defines a relation between the three sides of a right-triangle. It states that the square of larger side of the triangle(hypotenuse)  is equals to the sum of square of its other two sides(base and perpendicular).

It can be written as:

$\rm Hypotenuse^2 = Base^2 + Perpendicular^2$

On solving the given question, the correct statements obtained are:

- The radius of circle O is 13

- LP is a diameter of circle O.

- ∠$\rm LMP$ intercepts a semicircle.

To reach the above conclusions, following calculation is required:

The largest side of the Δ$\rm PML$ is $\RM PL$

Therefore,

$\begin{aligned} \rm PL^2 &= MP^2 + ML^2\\PL^2 &= 10^2 + 24^2\\PL^2 &= 100 + 576\\PL^2 &= 676\\PL &= \sqrt{676} \\PL &= 26\end$

Since, PL passes through the center of the circle, it is the diameter of the given circle.

Radius of the circle is half the diameter.

Hence radius of circle O will be $\dfrac{26}{2} = 13$.

Also diameter divides the circle into two semi-circles. Therefore the intercepting point of ∠$\rm LMP$ is a semi-circle.

Learn more about  Pythagoras' Theorem here:

https://brainly.com/question/343682