Prove the following theorems: Tangent segments drawn from an external point to the circle are congruent Given: A is the center of the circle. Tangents through external point D touch the circle at the points P and Q. To prove: seg DP ≅ seg DQ Construction: Draw seg AP and seg AQ. Proof: In ΔPAD and ΔQAD, seg PA ≅ seg QA …[Radii of the same circle] seg AD ≅ seg AD …[Common side] ∠APD = ∠AQD = 90° …[Tangent theorem] ∴ ΔPAD ≅ ΔQAD …[By Hypotenuse side test] ∴ seg DP ≅ seg DQ …[Corresponding sides of congruent triangles] Concept: Tangent Segment Theorem Is there an error in this question or solution?
True or False: Two tangent segments that meet outside of a circle are congruent. 1 Expert Answer
Zahid H. answered • 05/21/20 University Undergraduate with 2+ Years of Calculus Experience
Yes, this is always true. The Two-Tangent Theorem states that if two tangent segments are drawn to one circle from the same external point, then they are congruent. Since your question states that the two tangent segments meet, that means they're meeting at the same external point. |