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In figure, seg RS is a diameter of the c...

In figure, seg RS is a diameter of the circle with centre O. Point T lines in the exterior of the circle. Prove that `/_RTS` is an acute angle.

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Let seg RT intersect circle at point M. Draw seg MS.
Angle inscribed in a semicicle is a right angle
`:./_RMS=90^(@)`
`:. Seg SM bot " side " RT`
`:. triangle TMS` is a right angled triangle.
`:./_TMS+/_MTS+/_TSM=180^(@)" ""........"(" Sum of all angles of a triangle is " 180^(@))`
`:.90^(@)+/_MTS+/_TSM=180^(@)`
`:./_MTS+/_TSM=180^(@)-90^(@)`
`:./_MTS+/_TSM=90^(@)`
`:./_MTS lt 90^(@)`
i.e.`/_RTS lt 90^(@)" ""......."(" R-M-T ")`
`:./_RTS` is an acute angle`" ""........"(" By definition ")`
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