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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics - 2
8.6 Circles - Theorems

Statement: If two arcs are congruent, then their chords are equal.
Given: Arc ASB = Arc CTD
To prove: AB = CD

Proof: OA = OlC, OB = OlD (radii)
Angle AOB = Angle COlD (given that the arcs are congruent)
Hence by SAS Postulate on congruence AOB is congruent to COlD
Hence AB = CD

Statement: There is only one circle passing through three non collinear points.

Example: In the given figure prove that AB = CD

Solution: Arc BAD congruent Arc CDA
Hence Arc BAD - Arc AD = Arc CAD - Arc AD
Arc BA is congruent Arc CD
Hence AB = CD


Directions: Solve the following.
Q 1: BC is a chord of circle with centre O. A is a point on the major arc BC as shown, prove that angBAC + angOBC = 90.

Answer:

Question 2: This question is available to subscribers only!


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