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 Q 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:
CEF=DCF= 70 AEG+ 70 + 210 = 360 AEG= 80 In cyclic quadrilateral ABGE, ABG+AEG= 180 y + 80 = 180 y=100