# 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:
$\angle$OAD = 90o
$\angle$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:
$\angle$QTS = $\angle$RQS = 40o
$\angle$SQT = $\angle$QTS = 40o (isosceles triangle)
$\angle$PQT = 180o  – 40o – 40o = 100o
$\angle$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:
$\angle$BOD = 2 × $\angle$BED
= 2 × 35o = 70o
$\angle$ODB = $\angle$OBD
= (180– 70o÷ 2 = 55o

$\angle$ EDB = $\angle$ EBA = 75o

yo + $\angle$ 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: