The graph above shows a circle centred at the origin, O. The point P lies on the circle and has coordinates (30, -40). Line QR is a tangent to the circle passing through the point P.Name: Date:

Answer the following questions:

1) Calculate the distance OP

2) Hence write down the equation of the circle

3) Calculate the equation of the tangent line QR

4) The tangent line cuts the x-axis at point Q. Calculate the coordinates of point Q

5) Calculate the area of triangle OPQ to 1 d.p.

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2) The equation of the circle is 𝑥

3) The equation of the tangent line QR is y={\Large \frac{3}{4}}x-{\Large \frac{125}{2}}

4) Q =({\Large \frac{250}{3}}, 0)

5) 0.5 x 50 x 66.6666666667 ≈ 1666.7

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# Answers

1) Using Pythagoras, (OP)^{2}= (30)

^{2}+ (-40)

^{2}=> OP = 50

2) The equation of the circle is 𝑥

^{2}+ 𝑦

^{2}= 2500

3) The equation of the tangent line QR is y={\Large \frac{3}{4}}x-{\Large \frac{125}{2}}

4) Q =({\Large \frac{250}{3}}, 0)

5) 0.5 x 50 x 66.6666666667 ≈ 1666.7

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