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)
L O M = L N M = y o = 44 o y = 44 N M O = N L O = 41 o x o = 180 o 80 o 41 o = 59 o

(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)
A O B = 45 o × 2 = 90 o y o = 180 o 90 o = 90 o

(b)

A B D = 1 2 × 100 o = 50 o C D E = A B C = 85 o y o + 50 o = 85 o y o = 35 o y = 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)
A B E = A C D = 45 o y o = 180 o 45 o 55 o y o = 80 o y = 80
 
(b)
O M L = O L M = 42 o ( x o + 42 o ) + K N M = 180 o x o + 42 o + 110 o = 180 o x o + 152 o = 180 o x o = 180 o 152 o x o = 28 o x = 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

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