## zeesbrat3 3 years ago The figure below shows circle with center A. Segment BC is tangent to the circle at point B and segment CE is tangent to the circle at point E. The flow chart with missing reason proves that . Which missing reason should be filled in the blank space?

1. zeesbrat3

2. cwrw238

it UK we would put: 2 tangents to a given circle from one point outside the circle are equal in length in US in might be quoted differently

3. zeesbrat3

@cwrw238 These are my choices: Definition of a tangent line If two segments from the same interior point are tangent to the circle, then they are congruent. If two segments from the same exterior point are tangent to a circle, then they are congruent. Transitive Property

4. cwrw238

thats the third option then

5. zeesbrat3

ok, thank you so much!

6. zeesbrat3

think you can help me with one more?

7. cwrw238

yw

8. cwrw238

well i'll try...

9. zeesbrat3

The figure below shows Quadrilateral CDBE inscribed in a circle with center A. The paragraph proof with missing statement proves that its opposite angles are supplementary. Which statement can be used to fill in the blank space? Given that CDBE is a quadrilateral inscribed in a circle with center A, ∡DCE and ∡DBE are inscribed angles. Since the measure of an inscribed angle is one-half the measure of its intercepted arc, ∡DCE is half of arc DBE and ____________________. Since arc DBE and arc DCE add up to the whole circle, or 360 degrees, the total of ∡DCE and ∡DBE must be half of 360, or 180 degrees. Therefore, they are supplementary. By the definition of a quadrilateral, all interior angles must add to 360. Therefore, the other two angles must also be supplementary.

10. cwrw238

<DBE is half of arc DCE

11. zeesbrat3

Mind me asking how you find that? I want to learn how to find these answers, you know?