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prove that the line segment joining the points of contact of two |
| Answer» Given: l and m are the tangent to a circle such that l || m, intersecting at A and B respectively.To prove: AB is a diameter of the circle.Proof:A tangent at any point of a circle is perpendicular to the radius through the point of contact.{tex}\\therefore{/tex}\xa0{tex}\\angle X A O = 90 ^ { \\circ }{/tex}and\xa0{tex}\\angle Y B O = 90 ^ { \\circ }{/tex}Since\xa0{tex}\\angle X A O + \\angle Y B O = 180 ^ { \\circ }{/tex}\xa0An angle on the same side of the transversal is 180°.Hence the line AB passes through the centre and is the diameter of the circle. | |