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SPM Practice (Short Questions)

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Question 4:


In figure above, ABCD is a tangent to the circle CEF at point C. EGC is a straight line. The value of y is
 
Solution:
∠ C E F = ∠ D C F = 70 ∘ ∠ A E G + 70 ∘ + 210 ∘ = 360 ∘ ∠ A E G = 80 ∘ In cyclic quadrilateral A B G E , ∠ A B G + ∠ A E G = 180 ∘ y ∘ + 80 ∘ = 180 ∘ y = 100


Question 5:

In figure above, PAQ is a tangent to the circle at point A. AEC and BED are straight lines. The value of y is
 
Solution:
∠ABD = ∠ACD = 40o
∠ACB = ∠PAB = 60o
y= 180o  – ∠ACB – ∠CBD – ∠ABD
y= 180o  – 60o – 25o– 40o = 55o



Question 6:


In figure above, KPL is a tangent to the circle PQRS at point P. The value of x is

Solution:
∠PQS = ∠SPL= 55o
∠SPQ = 180o  – 30o – 55o= 95o
In cyclic quadrilateral,
∠SPQ + ∠SRQ = 180o
95o+ xo = 180o
x = 85o