Photo AI
In the diagram below, O is the centre of the circle - NSC Technical Mathematics - Question 9 - 2024 - Paper 2
Question 9
In the diagram below, O is the centre of the circle. OM = 3 cm and bisects AB. A, B and C are points on the circle such that AB = 10 cm. MN || BC. M is the midpoint ... show full transcript
Worked Solution & Example Answer:In the diagram below, O is the centre of the circle - NSC Technical Mathematics - Question 9 - 2024 - Paper 2
Step 1
Write down, with a reason, the size of \( M_i \).
Answer
Since line OM bisects AB and is drawn from the center of the circle to the midpoint of the chord, it is established that ( M_i = 90^\circ ). This follows from the property of a radius to a chord being perpendicular to the chord at its midpoint.
Step 2
Determine the length of the radius of the circle.
Answer
To find the length of the radius (( OA )), we can apply the Pythagorean theorem.
Let ( MB = 5 ) cm, and since ( OM = 3 ) cm, we can write:
[ OA^2 = OM^2 + MB^2 ]
[ OA^2 = 3^2 + 5^2 ]
[ OA^2 = 9 + 25 = 34 ]
[ OA = \sqrt{34} \approx 5.83 \text{ cm} ]
Step 3
If MN = 5,12 cm, write down, with a reason, the length of BC.
Answer
Since MN is parallel to BC and M is the midpoint of AB, by the properties of similar triangles or midsegments, we have:
[ BC = 2 \times MN = 2 \times 5.12 = 10.24 \text{ cm} ]
This shows that BC is twice the length of MN.