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A triangle ABC is inscribed in a circle....

A triangle ABC is inscribed in a circle. The bisector of angles BAC, ABC and ACB meet the circumcircle of the triangle at points P,Q and R respectively . Prove that :
(i) ` angle ABC = 2 angle APQ .`
(ii) `angle ACB = 2 angle APR `.
(iii) ` angle QPR = 90 ^(@) -(1)/(2) angle BAC. `

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ICSE-CIRCLES-EXERCISE 17(A)
  1. In the given figure AB is a diameter of the circle with centre O. DO i...

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  2. In the given figure, I is the incentre of Delta ABC BI when produce...

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  3. A triangle ABC is inscribed in a circle. The bisector of angles BAC, A...

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  4. Calculate the angles x,y and z if (x)/(3) = (y)/(4) =(z)/(5) (#...

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  5. In the given figure , AB = AC = CD and angle ADC = 38^(@) . Calculat...

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  6. In the given figure ,AC is the diameter of circle , centre O. Chord BD...

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  7. In the given figure ,AC is the diameter of the circle with centre O,C...

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  8. In the given figure . AE is the diamter of the circle . Write down the...

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  9. In the given figure. AOC is a diameter and AC is parallel to ED . If ...

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  10. Use in the given figure to find : (i) angle BAD . (ii) angle DQ...

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  11. In the given figure , AOB is a diameter and DC is parallel to AB . If ...

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  12. In the given figure ,AB is the diameter of a circle with centre O. an...

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  13. In the given figure, PQ is the diameter of the circle whose centre is ...

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  14. In the given figure, PQ is a diameter Chord SR is parallel to PQ . Giv...

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  15. AB is the diameter of the circle with centre O. OD is parallel to BC a...

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  16. In the given figures , the centre O of the small circle lies on the ci...

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  17. In the given figures , angle BAD = 65 ^(@) , angle ABD = 70 ^(@) and ...

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  18. In a cyclic quadrilateral ABCD angle A : angle C = 3: 1 and angle B...

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  19. The given figures shows a circle with centre O and angle ABP = 42 ^(...

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  20. In the given figure, M is the centre of the circle Chords AB and CD ar...

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