In the figure, chord AB= chord CD then complete the activity to prove arc ACE BD.
Activity :-
Chord AB~=CD .....(given)
Corresponding arcs of congruent chords of a circle are [ ]
Arc AB ~= arc [ ]
therefore m(arc AB) = m(arc CD)......... (1)
(arc addition postulate)
m(arc AC) + m(arc CB) = m(arc AB)
m(arc CB) + m(arc BD) = m(arc [ ])
From (1) and (2)
.. m(arc AC) + m(arc CB) = m(arc CB) + m(arc BD)
: m(arc AC) =[ ]
: arc AC = arc BD
Answers
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Answer:
Given : chord AB ≃ chord CD.
⇒ length (arc AB minor) = length (arc CD minor)
⇒ (arc AC) + (arc CB) = (arc CB) + (arc BD)
⇒ length of arc (AC) = length of arc (BD)
⇒ (arc AC) ≅ (arc BD)
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