8.1 Write down, with a reason, the size of $ar{S}$ - NSC Mathematics - Question 8 - 2017 - Paper 2
Question 8
8.1 Write down, with a reason, the size of $ar{S}$.
8.1.2 If the diameter is 20 cm and SP = 16 cm, calculate the length of TU.
8.2 ABC is a tangent to circle BQPR... show full transcript
Worked Solution & Example Answer:8.1 Write down, with a reason, the size of $ar{S}$ - NSC Mathematics - Question 8 - 2017 - Paper 2
Step 1
Write down, with a reason, the size of $ar{S}$
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Answer
Sˉ=90∘ (Angle in a semi-circle is a right angle)
Step 2
If the diameter is 20 cm and SP = 16 cm, calculate the length of TU.
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Answer
Given the diameter PR=20 cm, the radius QP=10 cm. Using the Pythagorean Theorem:
QT2=QP2−SP2
Substituting the values:
QT2=102−82=100−64=36
Therefore, QT=6 cm. The length of TU=QU−QT=10−6=4 cm.
Step 3
Calculate, with reasons, the size of $ar{B_1}$
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Answer
B1ˉ=30∘ (Tangent-chord theorem)
Step 4
Calculate, with reasons, the size of $ar{P_2}$
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Answer
P2ˉ=75∘ (Angles in the same segment are equal)
Step 5
Calculate, with reasons, the size of $ar{R}$
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Answer
Rˉ=180∘−30∘−70∘=80∘ (Sum of angles in a triangle)
Step 6
Calculate, with reasons, the size of $ar{Q_2}$
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Answer
Q2ˉ=15∘ (Opposite angles in cyclic quadrilateral)
