8.1 In the diagram, MP is a diameter of a circle centered at O - NSC Mathematics - Question 8 - 2021 - Paper 2
Question 8
8.1 In the diagram, MP is a diameter of a circle centered at O. MP cuts the chord NR at T. Radius NO and chords PR, MN and MR are drawn. \( R_1 = 69^\circ \).
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Worked Solution & Example Answer:8.1 In the diagram, MP is a diameter of a circle centered at O - NSC Mathematics - Question 8 - 2021 - Paper 2
Step 1
8.1.1 \( R_2 \)
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Answer
Since MP is the diameter of the circle, angle ( MRP ) is a right angle (90°) as per the inscribed angle theorem. Therefore, ( R_2 = 90° - 69° = 21° ).
Step 2
8.1.2 \( O_1 \)
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Answer
The angle at the center of the circle (( O_1 )) is twice the angle at the circumference (( R_2 )). Hence, ( O_1 = 2 \times R_2 = 2 \times 21° = 42° ).
Step 3
8.1.3 \( M_1 \)
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Answer
Since ( M_1 + N_1 = 180° - 138° ) (sum of angles in the same segment), we find that ( M_1 = 180° - 138° - N_1 = 21° ).
Step 4
8.1.4 \( M_2 \)
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Answer
Given that NO || PR, it follows that angles M2 and NRM are equal as they are alternate angles. Thus, ( M_2 = 48° ) as shown by ( \angle R = \angle N\hat{M}R ) resulting from equal sides MN and NR.
Step 5
8.2 Determine x
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