WAEC Mathematics Past Questions & Answers - Page 105

521.

The diagram is a circle of radius |QR| = 4cm. \(\bar{R}\) is a tangent to the circle at R. If TPO = 120^o, find |PQ|.

2.32cm

1.84cm

0.62cm

0.26cm

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Correct answer is C

No explanation has been provided for this answer.

522.

The diagram is a circle with centre P. PRST are points on the circle. Find the value of < PRS

144^o

72^o

40^o

36^o

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Correct answer is A

Reflex < POS = 2x (angle at centre is twice that at circumference)

reflex < POS + < POS = 350^o(angles at a point)

i.e. 2x + 8x = 360^o

10x = 360^o

x = \(\frac{360}{10}\)

= 36^o

< PRS = \(\frac{1}{2}\)

< POS(< at centre twice that circumference)

= \(\frac{1}{2}\) x 8x = 4x

4 x 36^o

< PRS = 144

523.

In the diagram, MN//PO, < PMN = 112^o, < PNO = 129^oo and < MPN = y^o. Find the value of y

51^o

54^o

56^o

68^o

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Correct answer is B

In \(\bigtriangleup\) NPO + PNO + PNO + < NOP = 180^o(sum of interior angles of a \(\bigtriangleup\) )

i.e. NPO + 129 + 37 = 180

< NOP = 180 - (129 + 37) = 14^o

< MNP = < NOP = 14^o (alt. < s)

In \(\bigtriangleup\) MPN

< PMN + < MNP + y = 180(sum of interior angles of a \(\bigtriangleup\))

i.e. 112 + 14 + y = 180^o

y = 180 - (112 + 14) = 180 - 126 = 54^o