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In the diagram, PX is a tangent to the circle and RST is an equilateral triangle...


Question

In the diagram, PX is a tangent to the circle and RST is an equilateral triangle. Calculate < PTS.

Options

A) 60o

B) 90o

C) 120o

D) 150o

The correct answer is C.

Explanation:

\(\bigtriangleup\) RST is equilateral triangle, hence

< TRS = < RTS = < RSt = 60o

But < PTR = 60o(Angle between a chord and a tangent at the point of contact = Angle in the alt. segment). From the diagram < PTS = < PTR + < RTS

= 60o + 60o = 120o


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Dicussion (1)

  • \(\bigtriangleup\) RST is equilateral triangle, hence

    < TRS = < RTS = < RSt = 60o

    But < PTR = 60o(Angle between a chord and a tangent at the point of contact = Angle in the alt. segment). From the diagram < PTS = < PTR + < RTS

    = 60o + 60o = 120o

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