# Class 10 Math Angles in a Segment of a Circle

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$1. Prove that in a given cyclic rilateral sum of opposite angles is two right angles and coiversely.$

$(ix) In the figure O is the centre of the circle then the angle x is:(a) 15^{\circ} (b) 30^{\circ} (c) 45^{\circ} (d) 60^{\circ}$

$(iii) In the adjacent figure if m \angle 3=75^{\circ} then find m \angle 1 and m \angle 2 .(a) 37 \frac{1}{2} 37 \frac{1}{2}^{\circ} (b) 37 \frac{1}{2}^{\circ} 75^{\circ} (c) 75^{\circ} 37 \frac{1}{2}^{\circ} (d) 75^{\circ} 75^{\circ}$

$(i) A circle passes through the vertices of a right angled \triangle A B C with m \overline{A C}=3 \mathrm{~cm} and m \overline{B C}=4 \mathrm{~cm} m \angle C=90^{\circ} . Radius of the circle is:(a) 1.5 \mathrm{~cm} (b) 2.0 \mathrm{~cm} (c) 2.5 \mathrm{~cm} (d) 3.5 \mathrm{~cm}$

$3. A O B and C O D are two intersecting chords of a circle. Show that \triangle^{s} A O D and B O C are equiangular.$

$4. \overline{A D} and \overline{B C} are two parallel chords of a circle. Prove that arc A B \cong \operatorname{arc} C D and arc A C \cong \operatorname{arc} B D .$