Circles Short Questions (Question 1 – 4)


Question 1:
In figure above, FAD is a tangent to the circle with centre O. AEB and OECD are straight lines. The value of y is

Solution:

OAD = 90o
AOD= 180o  – 90o – 34o= 56o
y = 56o  ÷ 2 = 28o



Question 2:
In figure above, PQR is a tangent to the circle QSTU at and TUPV is a straight line. The value of y is

Solution:

QTS = ∠RQS = 40o
SQT= ∠QTS = 40o (isosceles triangle)
PQT= 180o  – 40o – 40o= 100o
TPQ= 180o  – 115o = 65o
y = 180o  – 100o – 65o= 15o



Question 3:
In figure above, ABC is a tangent to the circle BDE with centre O, at B.
Find the value of y.
 
Solution:
BOD= 2 × ∠BED
= 2 × 35o = 70o
ODB = ∠OBD
= (180– 70o÷ 2 = 55o

EDB = ∠ EBA = 75o
yo + ∠ ODB = 75o
yo + 55o = 75o
y = 20o



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

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