-Use the drawing provided to explain why the following theorem is true.
"The tangent segments to a circle from an external point are congruent."
Given: and are tangent to Prove: [Hint: Use auxiliary line segment .]

Question

-Use the drawing provided to explain why the following theorem is true.
"The tangent segments to a circle from an external point are congruent."
Given:  and  are tangent to  Prove:  [Hint: Use auxiliary line segment  .]

Quizplus · Accepted Answer

The Answer is Draw Draw . Now and because the measure of an angle formed by a tangent and chord at the point of contact is one-half the measure of the intercepted arc. Then by substitution, so . Then because these sides lie opposite the congruent angles of .

Draw . Now and because the measure of an angle formed by a tangent and chord at the point of contact is one-half the measure of the intercepted arc. Then by substitution, so . Then because these sides lie opposite the congruent angles of .

. Now

and

because the measure of an angle formed by a tangent and chord at the point of contact is one-half the measure of the intercepted arc.
Then Draw . Now and because the measure of an angle formed by a tangent and chord at the point of contact is one-half the measure of the intercepted arc. Then by substitution, so . Then because these sides lie opposite the congruent angles of .

by substitution, so Draw . Now and because the measure of an angle formed by a tangent and chord at the point of contact is one-half the measure of the intercepted arc. Then by substitution, so . Then because these sides lie opposite the congruent angles of .

. Then

because these sides lie opposite the congruent angles of Draw . Now and because the measure of an angle formed by a tangent and chord at the point of contact is one-half the measure of the intercepted arc. Then by substitution, so . Then because these sides lie opposite the congruent angles of .

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-Use the Drawing Provided to Explain Why the Following Theorem