Prove that the tangent drawn at the ends of a chord of a circle make equal angles with the chord

Prove that the tangent drawn at the ends of a chord of a circle make e

1.	Prove that the tangent drawn at the ends of a chord of a circle make equal angles with the chord
Answer» Let NM be chord of circle with centre C.Let tangents at M.N meet at the point O.Since OM is a tangent{tex}\\therefore OM \\bot CM{/tex}\xa0i.e.\xa0{tex}\\angle OMC = 90^\\circ {/tex}{tex}\\because ON{/tex}\xa0is a tangent{tex}\\therefore ON \\bot CN{/tex}\xa0i.e.\xa0{tex}\\angle ONC = 90^\\circ {/tex}Again in {tex}\\triangle CMN.CM = CN = r{/tex}{tex}\\therefore \\angle CMN = \\angle CNM{/tex}{tex}\\therefore \\angle OMC - \\angle CMN = \\angle ONC - \\angle CNM{/tex}{tex} \\Rightarrow \\angle OML = \\angle ONL{/tex}Thus, tangents make an equal angle with the chord.