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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics - 2
8.5 Angle at Centre Theorem

: Angle subtended by an arc at the centre is twice the angle subtended by the angle at the circumference.

Given: ACB is the major arc of the circle. Angles AOB and ACB stand on the same arc.
To prove: Angle AOB = 2 Angle ACB
Proof: From triangle AOC, x = a+a (Exterior angle of a triangle)
Hence x = 2a
From triangle OBC, y = b+b
Hence y = 2b
Angle AOB = x + y
Hence angAOB = 2(a+b)
Hence Angle AOB = 2 Angle ACB

Example: Find angle a.

Angle at circumference = 1/2 angle at centre.
Angle a = 70o
Answer: 70o


Directions: Solve the following
Q 1:
Answer:

Q 2:
Answer:

Q 3:
Answer:

Q 4: If the sum of the angles at the circumference and the centre is 120 degrees. Find the angle at centre.
40o
80o
70o

Q 5:
Answer:

Q 6: If one angle at the circumference of a circle is 55 degrees , find the angle at centre.
55o
100o
110o

Q 7:
Answer:

Q 8: Consider triangle ABC inscribed in a circle, if ang ABC is 50 degrees and is in the major arc, what is the angle at the centre.
75o
100o
50o

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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