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).

In figure 3.37, points G, D, E, F are concyclic points of a circle with centre C. \(\angle ECF = 70^\circ\), m(arc DGF) = \(200^\circ\) find m(arc DE) and m(arc DEF).

Figure: Radii CD, CE, CF are drawn. Going round the circle the points are D, G, F, E; arc DGF contains G, and E lies on the other arc DF.

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Answer: m(arc DE) = \(90^\circ\), m(arc DEF) = \(160^\circ\)

Arcs DGF and DEF together make the whole circle:

\[m(\text{arc DEF}) = 360^\circ - 200^\circ = 160^\circ\]

The measure of a minor arc equals its central angle, so m(arc EF) = \(\angle ECF = 70^\circ\).

\[m(\text{arc DE}) = m(\text{arc DEF}) - m(\text{arc EF})\] \[= 160^\circ - 70^\circ = 90^\circ\]

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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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).

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