Question

Type the correct answer in the box. circle centered at o has points a, c, and c on its circumference. diameter oab and chords ac and bd are drawn, forming triangle abc. suppose ac = 5 cm, bc = 12 cm, and . to the nearest tenth of a unit, the radius of the circumscribed circle is cm and m?oac = �. reset next

Answer 1

To find the radius of the circle, we can use the property that the perpendicular bisectors of the sides of a triangle intersect at the center of the circumscribed circle.

Step-by-step explanation:

To find the radius of the circle, we can use the property that the perpendicular bisectors of the sides of a triangle intersect at the center of the circumscribed circle.

Since AC and BD are chords of the circle, the perpendicular bisectors of AC and BD will intersect at the center of the circle.

By constructing the perpendicular bisectors of AC and BD, we find that they intersect at O, the center of the circle. The radius of the circumscribed circle is equal to the distance from O to any of the points A, B, or C.

To find the radius, we can use the Pythagorean Theorem in triangle OAC: (radius)^2 = (1/2 * AC)^2 + OC^2. Substituting the given length of AC and the unknown radius, we can solve for the radius of the circle.

Answer 2

The radius of the circumscribed circle is 6.5 cm.

The measure of angle OAC is 67.4°.

Since AB is represents the diameter of the given circle centered at O, we can reasonably infer and logically deduce that inscribed angle C must be a right angle with a measure of 90 degrees.

In order to determine the length of diameter AB, we would have to apply Pythagorean's theorem as follows;

`AB^2 = AC^2 + BC^2\\\\ AB = √(5^2 +12^2) \\\\AB=√(25+144)`

AB = 13 cm.

In Mathematics, the radius of a circle is half the length of the diameter;

OA = AB/2

OA = 13/2

OA = 6.5 cm.

Based on the diagram, the measure of inscribed angle B is one-half the measure of arc AC;

m∠B = 45.2°/2

m∠B = 22.6°

Now, we can determine measure of angle OAC by using the complementary angles property;

m∠B + m∠OAC = 90°

m∠OAC = 90° - 22.6°

m∠OAC = 67.4°.

Complete Question:

Suppose AC = 5 cm, BC = 12 cm, and mAC = 45.2°.

To the nearest tenth of a unit, the radius of the circumscribed circle

is __?__ cm and m∠OAC = __?__°.