Q1 of 59 Page 63

In figure 3.37, points G, D, E, F are concyclic points of a circle with centre C.

∠ ECF = 70°, m(arc DGF) = 200° find m(arc DE) and m(arc DEF).



Given ∠ECF = 70° and m(arc DGF) = 200°


We know that measure of major arc = 360° - measure of minor arc


m(arc DGF) = 360° - m(arc DF)


⇒ m(arc DF) = 360° - 200° = 160°


⇒∠ DCF = 160°


∵ The measure of a minor arc is the measure of its central angle.


∴m(arc DEF) = 160°


So, ∠DCE = ∠ DCF -∠ECF = 160° - 70°


⇒ ∠DCE = 90°


The measure of a minor arc is the measure of its central angle.


m(arc DE) = 90°


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