Understanding the theorem on arcs of circles. Click on the Link to Watch the VIDEO explanation:
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Theorem on Arcs of a circle.
In equal circles or in a same circles, if two arcs are subtend equal angles at the centers, they are equal.
Given AXB and CYD are equal circles with centres P and Q; arcs AMB and CND subtend equal angles angle APB and angle CQD.
To prove is that arc AMB is equal to arc CND
Proof is as follows:
Apply circle CYD to circle AXB so that centre Q falls on the centre P and QC along PA and D on the same side as B. Therefore, circle CYD overlaps circle AXB.
Therefore, C falls on A. Since circles are equal
Angle APB is equal to angle CQD. Given
Therefore, QD falls along PB.
Watch Video
Theorem on Arcs of a circle.
In equal circles or in a same circles, if two arcs are subtend equal angles at the centers, they are equal.
Given AXB and CYD are equal circles with centres P and Q; arcs AMB and CND subtend equal angles angle APB and angle CQD.
To prove is that arc AMB is equal to arc CND
Proof is as follows:
Apply circle CYD to circle AXB so that centre Q falls on the centre P and QC along PA and D on the same side as B. Therefore, circle CYD overlaps circle AXB.
Therefore, C falls on A. Since circles are equal
Angle APB is equal to angle CQD. Given
Therefore, QD falls along PB.
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