Geo EOC Review #6 (Circles)

Triangle ABC is inscribed in circle O. Segment AB is the diameter of the circle. If $$m\angle ABC=17.5$$ , what is the measure of $$\angle BAC?$$

Which statement must be true about the figure?

In the circle below, $$m\angle DEF=\left(5x-10\right)\degree.\$$ What is the value of x?

(a)  

Points A, B, and D lie on circle D. Determine the measure of each indicated angle given that $$m\angle A=30\degree.$$

$$m\angle BCD=$$ ​ ​ (a)   °

$$m\angle ABD=$$ ​ (b)   °

In the diagram, quadrilateral PQRS is inscribed in circle O. Match each statement with the correct value.

A support structure is being created to stabilize circular playground. The outline of the support structure is represented as quadrilateral ABCD as shown. The park planner needs to know the relationship between the opposite angles of the inscribed quadrilateral. Which of the following relationships are correct? Select All That Apply!

In the diagram below of circle O, chords $$\overline{AB\ }and\ \overline{CD}$$ intersect at E. If CE = 10, ED = 6, and AE = 4, what is the length of EB? Enter NUMBERS only!

(a)  

n the diagram below of circle O, chords $$\overline{AB\ }and\ \overline{CD}$$ intersect at E. If CE = 3, ED = 2x+8, and AE = 4x-3, and EB = 4? What is the value of x?

In the figure, $$\overline{AB}$$ and $$\overline{AC}$$ are secants. What is the value of x?

In the figure, $$\overline{AB}\ and\ \overline{AC}\$$ are secants. Find the length of $$\overline{AC}$$ .