3.2.1 Circles II, PT3 Practice


3.2.1 Circles II, PT3 Practice

Question 1:
(a) In Diagram below, KLMLPN and MPO are straight lines.

 
Find the value of x and of y.

(b) In the diagram below, O is the centre of the circle. Find the value of

(i) x   (ii) y
 
Solution:
(a)
LOM=LNM=yo=44oy=44NMO=NLO=41oxo=180o80o41o=59o

(b)(i)
2x = 200o
x = 100o

(b)(ii)
+ y = 180o
100o + y = 180o
y = 80o


Question 2:
(a) In Diagram below, AOC and BCD are straight lines with centre O.
Find the value of y.

(b) In diagram below, ABCD is a circle with centre O and ADE is a straight line.

Find the value of y.

Solution:
(a)
AOB=45o×2=90oyo=180o90o=90o

(b)

ABD=12×100o=50oCDE=ABC=85oyo+50o=85oyo=35oy=35


Question 3:
(a)  In diagram below, ABCD is a circle. AEC and BED are straight lines.
 
Find the value of y.
 
(b) Diagram below shows a circle KLMN with centre O.
 
Find the value of x.

Solution:
(a)
ABE=ACD=45oyo=180o45o55oyo=80oy=80
 
(b)
OML=OLM=42o(xo+42o)+KNM=180oxo+42o+110o=180oxo+152o=180oxo=180o152oxo=28ox=28


Question 4:
Diagram below shows a semicircle ABCD with centre O.

It is given that AB = CD.
Find the value of y.

Solution:
y+ 32o + 32o + 90o = 180o
y= 180o – 154o
y= 26o
= 26


Question 5:
In diagram below, ABC and DEF are straight lines.

Find the value of x and of y.

Solution:
x+38=93        x=9338        x=55DBG=38o (GB=GD)       yo=DBG    y=38