In the following figure, point G, D, E, F are concyclic points of a circle with centre C. \(\angle ECF = 70^\circ\), \(m(\text{arc } DGF) = 200^\circ\). Find \(m(\text{arc } DE)\).[Figure: circle with centre C; D in the upper left, G in the upper rig…

Q.2 (B)(iii) In the following figure, point G, D, E, F are concyclic points of a circle with centre C. \(\angle ECF = 70^\circ\), \(m(\text{arc } DGF) = 200^\circ\). Find \(m(\text{arc } DE)\).

[Figure: circle with centre C; D in the upper left, G in the upper right, E in the lower left and F in the lower right on the circle; segments CD, CE and CF are drawn, with \(\angle ECF\) marked at C.]

Doubtly Asked 25 Oct 2026 ssc 10th Save WhatsApp Report

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Answer: \(m(\text{arc } DE) = 90^\circ\)

\(m(\text{arc } DGF) + m(\text{arc } DEF) = 360^\circ\) (the two arcs together make the complete circle).

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

\(\angle ECF\) is a central angle, so \(m(\text{arc } EF) = m\angle ECF = 70^\circ\).

Now arc DEF is made of arc DE and arc EF:
\(m(\text{arc } DE) = 160^\circ - 70^\circ = 90^\circ\).

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report

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In the following figure, point G, D, E, F are concyclic points of a circle with centre C. \(\angle ECF = 70^\circ\), \(m(\text{arc } DGF) = 200^\circ\). Find \(m(\text{arc } DE)\).[Figure: circle with centre C; D in the upper left, G in the upper rig…

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