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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.

A) 60o

B) 90o

C) 120o

D) 150o

### 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

## 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