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In the diagram, PQRS is a cyclic quadrilateral - NSC Mathematics - Question 9 - 2021 - Paper 2

Question 9

In the diagram, PQRS is a cyclic quadrilateral. PS is produced to W. TR and TS are tangents to the circle at R and S respectively. $ ilde{T}=78^{ ext{o}}$ and $ ilde... show full transcript

Worked Solution & Example Answer:In the diagram, PQRS is a cyclic quadrilateral - NSC Mathematics - Question 9 - 2021 - Paper 2

Step 1

Give a reason why ST = TR.

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Answer

ST = TR because they are tangents from the same point (point T) to the circle at points S and R.

Step 2

Calculate, giving reasons, the size of: $S_2$

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Answer

$S_2 = 51^{ ext{o}}$

( $ext{Angles opposite equal sides are equal}$ .)

Step 3

Calculate, giving reasons, the size of: $S_3$

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Answer

$S_3 = 42^{ ext{o}}$

( $ext{Using the property of cyclic quadrilaterals (exterior angle) or} ewline$ S_3 = 180^{ ext{o}} - (87^{ ext{o}} + 51^{ ext{o}})$.)

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