A and B are points on the circumference of a circle, centre O - OCR - GCSE Maths - Question 13 - 2017 - Paper 1
Question 13
A and B are points on the circumference of a circle, centre O.
CA and CB are tangents to the circle.
Prove that triangle OAC is congruent to triangle OBC.
Worked Solution & Example Answer:A and B are points on the circumference of a circle, centre O - OCR - GCSE Maths - Question 13 - 2017 - Paper 1
Step 1
OC is common or shared
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Answer
In triangles OAC and OBC, the side OC is common to both triangles, serving as one of the equal sides.
Step 2
OA = OB (equal radii)
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Answer
Since both OA and OB are radii of the same circle, they are equal: OA = OB.
Step 3
∠OAC = ∠OBC (tangent and radius)
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Answer
The angle ∠OAC is equal to ∠OBC because they are both angles formed between a tangent and a radius at points A and B respectively, leading to ∠OAC = ∠OBC.
Step 4
Conclusion
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Answer
By the criteria of Side-Angle-Side (SAS), where we have:
OC as a common side.
OA = OB.
∠OAC = ∠OBC,
we can conclude that triangle OAC is congruent to triangle OBC. Therefore, we can write: OAC ≅ OBC.
