SPM Practice (Short Questions)

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:

\begin{array}{l} ∠ C E F = ∠ D C F = 70^{\circ} \\ ∠ A E G + 70^{\circ} + 210^{\circ} = 360^{\circ} \\ ∠ A E G = 80^{\circ} \\ In cyclic quadrilateral A B G E, \\ ∠ A B G + ∠ A E G = 180^{\circ} \\ y^{\circ} + 80^{\circ} = 180^{\circ} \\ y = 100 \end{array}

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 = 40^o

∠ACB = ∠PAB = 60^o

y= 180^o– ∠ACB – ∠CBD – ∠ABD

y= 180^o– 60^o – 25^o– 40^o = 55^o

Question 6:

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

Solution:

∠PQS = ∠SPL= 55^o

∠SPQ = 180^o– 30^o – 55^o= 95^o

In cyclic quadrilateral,

∠SPQ + ∠SRQ = 180^o

95^o+ x^o = 180^o

x = 85^o