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A, B, C and D are points on the circumference of a circle, centre O - Edexcel - GCSE Maths - Question 13 - 2018 - Paper 2
Question 13
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 st... 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 13 - 2018 - Paper 2
Step 1
Show that $y - x = 90$
Answer
To show that , we can reference properties of angles in a circle:
- The angle is the angle at point inscribed in the circle, which subtends arc .
- The angle is the angle at point which subtends the same arc , but it lies outside of the circle.
- According to the Alternate Segment Theorem, we know that an angle formed by a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
Hence, we can conclude: which means: $$y - x = 90.$
Step 2
Is Dylan correct?
Answer
Dylan is not correct. The values he proposed are not possible within the context of the circle's angles.
Specifically, since must be an angle inside a triangle, it cannot exceed 180 degrees. If , this violates the triangle condition that any angle must be less than 180 degrees. Therefore, the assertion cannot hold true with the values Dylan suggested.