Respuesta :

boffeemadrid

Answer:

(C)

Step-by-step explanation:

Given: BC is tangent to the circle A at D.

To prove: AB is congruent to AC

Proof:

Statements                                                            Reason

1. BC is tangent to the circle A at D.                     Given

2. DB≅DC                                                               Given

3.AD⊥BC               If a line is tangent to a circle then it is perpendicular to the radius at the point of tangency.

4. ∠ADB and ∠ADC are right angles     Definition of perpendicular lines

5. ∠ADB≅∠ADC                                      Right angles are congruent

6. AD≅AD                                                Reflexive property of congruence

7. ΔADB≅ΔADC                                      SAS rule

8. AB≅AC                                                CPCTC

Hence, option (C) is correct.

Tangent to a circle is straight line just touching the circle at one point. The reason to complete the proof is: If a line is tangent to a circle,  then it is perpendicular to the point of tangency

What is tangent to a circle?

A line segment which touches a circle specified to only one point is called a tangent to that circle.


How are radius and tangent to a circle related?

There is a theorem in mathematics that:

If there is a circle O with tangent line L intersecting the circle at point A, then the radius OA is perpendicular to the line L.

For the given case, the missing statement for the proof is:

If a line is tangent to a circle,  then it is perpendicular to the point of tangency(the point on circle where the tangent intersects it).

Hence, the reason to complete the proof is: If a line is tangent to a circle,  then it is perpendicular to the point of tangency


Learn more about tangent here:

https://brainly.com/question/1503247

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