Question

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

∠ECF = 70°, m(arc DGF) = 200°

Find m(arc DEF) by completing activity.

m(arc EF) = ∠ECF     ......[Definition of measure of arc]

∴ m(arc EF) = `square`

But; m(arc DE) + m(arc EF) + m(arc DGF) = `square`   .....[Measure of a complete circle]

∴ m(arc DE) = `square`

∴ m(arc DEF) = m(arc DE) + m(arc EF)

∴ m(arc DEF) = `square`

Answer 1

m(arc EF) = ∠ECF       ...[Definition of measure of arc]

∴ m(arc EF) = 70°      ...(i)

But; m(arc DE)+ m(arc EF) + m(arc DGF) = 360°    ...[Measure of a complete circle]

∴ m(arc DE) + 70° + 200° = 360°

m(arc DE) = 360° – 270°  ...[From (i) and given]

∴ m(arc DE) = 90°           ...(ii)

∴ m(arc DEF) = m(arc DE) + m(arc EF)

= 90° + 70°       ...[From (i) and (ii)]

∴ m(arc DEF) = 160°