A, B, C and D are points on the circumference of a circle, centre O. FDE is a tangent to the circle. a) Show that $y - x = 90$ You must give a reason for each stage of your working. Dylan was asked to give some possible values for $x$ and $y$. He said, "$y$ could be 200 and $x$ could be 110, because 200 - 110 = 90" b) Is Dylan correct? You must give a reason for your answer.

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A, B, C and D are points on the circumference of a circle, centre O - Edexcel - GCSE Maths - Question 14 - 2018 - Paper 2

Question 14

A, B, C and D are points on the circumference of a circle, centre O. FDE is a tangent to the circle. a) Show that $y - x = 90$ You must give a reason for each stage... show full transcript

Worked Solution & Example Answer:A, B, C and D are points on the circumference of a circle, centre O - Edexcel - GCSE Maths - Question 14 - 2018 - Paper 2

Step 1

Show that $y - x = 90$

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Answer

To demonstrate that $y - x = 90$ , we start by analyzing the angles within the circle. We know that the angle subtended by a tangent to a circle is equal to the angle in the alternate segment formed by the diameter. Therefore:

Since FDE is a tangent to the circle at point D, we have that $y$ (the angle at point D) corresponds to an angle in the alternate segment, which means $y = 90 + x$ .
Reorganizing gives us $y - x = 90$ . Thus, we have shown that $y - x = 90$ .

Step 2

Is Dylan correct?

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Answer

Dylan is not correct. Although he provided the calculation of $200 - 110 = 90$ , the values of $y$ and $x$ must represent angles in a triangle. Angles in a triangle must be less than 180 degrees. Given that $y$ is stated as 200 degrees, this is not a valid angle in geometry. Thus, it follows that Dylan's reasoning is flawed.

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