Question

Which statements about circle O are true? Select three options. 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

Answer: A) The radius of circle O is 13.

C) LP is a diameter of circle O.

D) ∠LMP intercepts a semicircle.

Explanation:

om edge

Answer 2

The radius of circle O is 13

LP is a diameter of circle O.

∠LMP intercepts a semicircle.

Explanation:

The missing image is attached in the diagram below.

From the diagram;

we can determine the length LP by using the Pythagoras theorem.

i.e.

hypotenuse² = opposite² + adjacent²

LP² = ML² + MP²

LP² = 24² + 10²

LP² = 576 + 100

LP =
`√(676)`

LP = 26

Since line LP cuts the circle into two equal halves, we can say the line LP is the diameter of circle O.

if the diameter (LP) = 26

Then, the radius r = 26/2 = 13

The radius of circle O is 13.

Similarly, the arc LMP is 180° (∵ inscribed angle is 1/2 the measure of central angle), and LMP is 180°, then ∠LMP intercepts a semicircle.