Circles Short Questions (Question 5 – 8)


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= 180– ∠ACB – ∠CBD – ∠ABD
y= 180– 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 = 180– 30o – 55o= 95o
In cyclic quadrilateral,
SPQ + ∠SRQ = 180o
95o+ xo = 180o
x = 85o


Question 7:
In figure above, APB is a tangent to the circle PQR at point P. QRB is a straight line. The value of x is

Solution:
PQR = ∠RPB= 45o
QPR = (180– 45o) ÷ 2 = 67.5o
PQR + ∠BPQ + xo = 180o
45o+ (67.5o + 45o) + xo = 180o
x = 22.5o


Question 8:
The figure above shows two circles with respective centres O and V. AB is a common tangent to the circles. OPRV is a straight line. The length, in cm, of PR is 

Solution:



cos 86 o = O M O V 0.070 = 1 O V O V = 1 0.070 O V = 14.29 c m P R = 14.29 5 4 = 5.29 c m

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