Prove that the tangents drawn at the ends of a circle make equal angle

1.	Prove that the tangents drawn at the ends of a circle make equal angles with the chord
Answer» Let NM be chord of circle with centre C.Let tangents at MN meet at the point O.Since OM is a tangent∴ MO ⊥ CM i.e. ∠OMC = 90°∵ ON is a tangent∴ ON ⊥ CN\xa0i.e. ∠ONC = 90° Again in ΔCMN , CM = CN = r\xa0∴ ∠CMN = ∠CNM∴ ∠OMC – ∠CMN = ∠ONC – ∠CNM⇒ ∠OML = ∠ONLThus, tangents make equal angle with the chord.

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