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Class 10 Math Angles in a Segment of a Circle


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Class 9Class 10First YearSecond Year
(iv)GiventhatOisthecentreofthecircle.Theanglemarkedxwillbe:(a)1212(b)25(c)50(d)75(iv) Given that O is the centre of the circle. The angle marked x will be:(a) 12 \frac{1}{2}^{\circ} (b) 25^{\circ} (c) 50^{\circ} (d) 75^{\circ}

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

1.Provethatinagivencyclicrilateralsumofoppositeanglesistworightanglesandcoiversely.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}
(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}

(ix)InthefigureOisthecentreofthecirclethentheanglexis:(a)15(b)30(c)45(d)60(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}
(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}

(iii)Intheadjacentfigureifm3=75thenfindm1andm2.(a)37123712(b)371275(c)753712(d)7575(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}
(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}

(i)AcirclepassesthroughtheverticesofarightangledABCwithmAC=3 cmandmBC=4 cmmC=90.Radiusofthecircleis:(a)1.5 cm(b)2.0 cm(c)2.5 cm(d)3.5 cm(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.
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.

3.AOBandCODaretwointersectingchordsofacircle.ShowthatsAODandBOCareequiangular.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 .
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 .

4.ADandBCaretwoparallelchordsofacircle.ProvethatarcABarcCDandarcACarcBD.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 .

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