Understanding the theorem on circles. Click on the Link to Watch the VIDEO explanation:
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Theorem 4
In equal circles or in the same circles if two arcs are equal, the chords of the arc are equal.
Given : In equal circles AXB and CYD, with centers P and Q respectively have an arc AMB is equal to CND.
To prove : The chord AB is equal to chord CD
Construction : Join AP, BP, CQ and DQ.
In triangles ABP and CDQ, AP is equal to CQ and BP is equal to DQ since they are the radii of equal circles.
Angle APB is equal to angle CQD since arc AMB is equal to arc CND.
Therefore, triangles ABP is congruent to triangle CDQ by S.A.S postulates.
Therefore, AB is equal to CD.
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Theorem 4
In equal circles or in the same circles if two arcs are equal, the chords of the arc are equal.
Given : In equal circles AXB and CYD, with centers P and Q respectively have an arc AMB is equal to CND.
To prove : The chord AB is equal to chord CD
Construction : Join AP, BP, CQ and DQ.
In triangles ABP and CDQ, AP is equal to CQ and BP is equal to DQ since they are the radii of equal circles.
Angle APB is equal to angle CQD since arc AMB is equal to arc CND.
Therefore, triangles ABP is congruent to triangle CDQ by S.A.S postulates.
Therefore, AB is equal to CD.
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