9. If JG = JF, GD = 13, and mCD = 136,
find each measure.
Answers
Given :- JG = JF, GD = 13, and mCD = 136° .
Solution :-
A) ED = ?
since JG ⟂ chord ED .
→ EG = GD { Perpendicular from centre to the chord bisects the chord. }
so,
→ ED = EG + GD
→ ED = 13 + 13 { given that, GD = 13. }
→ ED = 26 (Ans.)
B) CF = ?
given that, JG = JF .
so,
→ CD = ED { chord which are at equal distance from the centre are equal in length .}
therefore,
→ CF = (1/2)CD = 26/2 = 13 (Ans.)
also,
→ ED = CD
then,
→ m(ED) = m(CD)
→ m(ED) = 136° (Ans.)
now, FH bisects m(CD) .
so,
→ m(HD) = (1/2) * m(CD) = (1/2) * 136° = 68° (Ans.)
therefore,
→ m(CE) = 360° - [m(CD) + m(ED)] { Length of all arcs is equal to 360°. }
→ m(CE) = 360° - (136° + 136°)
→ m(CE) = 360° - 272°
→ m(CE) = 88° (Ans.)
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