College Geometry

Question

⊙D is shown below. 

Which of the following statements are true? 

Create an answer using the numbers associated with the true statements. For example, if only 1, 2, and 5 are true, then the answer is 125; if only 3 and 5 are true, then the answer is 35, etc.

If a given statement does not contain names of geometrical objects, it is a general statement about circles and is not necessarily related to the diagram.

1.   BA−→ is a secant of ⊙D.

2.   If two parallel lines intersect a circle, the intercepted arcs between those lines are congruent.

3.   m∠ABE=mAH⏜

4.   CH−→− is a tangent of ⊙D.

5.   A secant is a line (segment, or ray) that intersects a circle in exactly one point.

6.   A tangent of a circle is perpendicular to the radius at the point of tangency.

7.   m∠ABF=12⋅mAB⏜

a) 1267

b) 12467

c) 1237

d) 25

e) 267

f) 136

g) None of the above

Answer 1

1. Ray BA is a secant of Circle D. A secant intersects a circle in exactly 2 points. So 1 is true. Answer so far: 1
2. True, since parallel lines are the same distance apart when they intersect the circle on one side as when the intersect the circle on the other side. So this is TRUE. Answer so far: 12
3. This is false. Since Angle is an INSCRIBED angle, it is half the measure of the arc. Answer so far: 12
4. This is false. A tangent line touches the circle in only one point. Answer so far: 12
5. False. A secant intercepts a circle in exactly two points. Answer so far: 12
6. TRUE. Answer so far: 126
7. If it says mAngleABF = (1/2) mArcAB, then this is true. Final Answer is 1267

This is Answer Choice A

(if #7 said something different, it may not be true. could not tell from the way it was typed.)