Question: topic: theorem on angles formed by tangents and secants Given: KL and KM are tangent and secant segments, respectively, of OO drawn from exterior point

topic: theorem on angles formed by tangents and secants

Given: KL and KM are tangent and secant segments, respectively, of OO drawn from exterior point K. O KM intersects OO at N. Prove: (KL)2 = KM KN Draw LM and LN so that we formed two similar triangles. Then show the proof using the Two-Column Proof. Proof: Statement Reason mZNLK = (m N ) and (1) MZLMN = 2 (m LN mZNLK = mZLMN (2) ZNLK = ZLMN (3) mZLNK = mZNLM + mzLMN (4) mzLNK = mZNLM + mzNLK (5) mZKLM = mZNLM + mzNLK (6) mZLNK = mZKLM (7) LLNK - ZKLM (8) 4 MKL (9) KM KL KI. KN 10. Lengths of sides of similar triangles are KM KN = ILKI 2

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