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If O is the circumcentre of a A B C a...

If `O` is the circumcentre of a ` A B C` and `O D_|_B C ,` prove that `/_B O D=/_Adot`

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Proof: Arc BC subtends `angleBOC` at the centre and `angleBAC` at the remaining part at the circle.
`angleBOC=2angleA`___1
In right `triangleOBD` and `triangleOCD`
`OD=OD` (common)
Hyp. `OB=OC` (radii of the circle)
`angleOBD=angleOCD` (each `90^@`)
...
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RD SHARMA-CIRCLE -All Questions
  1. In Figure, chord E D is parallel to the diameter A C of the circ...

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  2. In Figure, A B\ a n d\ C D are two chords of a circle, intersecting...

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  3. If O is the circumcentre of a A B C and O D|B C , prove that /B O ...

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  4. In the given figure, a diameter PQ of a circle bisects the chord RS at...

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  5. In Figure, A B=C Ddot Prove that B E=D E\ a n d\ A E=C E , where E is ...

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  6. Two diameters of a circle intersect each other at right angles. Prove ...

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  7. Prove that the circle drawn with any side of a rhombus as a diameter, ...

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  8. A Ca n dB D are chords of a circle that bisect each other. Prove that:...

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  9. A Ca n dB D are chords of a circle that bisect each other. Prove that:...

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  10. A B C and A D C are two right triangles with common hypotenuse A Cdot ...

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  11. D is a point on the circumcircle of A B C in which A B=A C such tha...

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  12. The bisector of /B of an isosceles triangle A B C with A B=A C mee...

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  13. Bisectors of angles A, B and C of a triangle ABC intersect its circum...

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  14. Prove that the mid-point of the hypotenuse of a right triangle is eq...

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  15. A B is a diameter of a circle with centre O and radius O D is perp...

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  16. In Figure, P , is any point on the chord B C of a circle such that A B...

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  17. In Fig. 10.32, AB is a diameter of the circle, CD is a chord equal ...

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  18. In Figure, O is the centre of the circle. If /A P B=50^0, find /A O B\...

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  19. In Figure, it is given that O is the centre of the circle and /A...

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  20. In Figure, O is the centre of the circle. Find /B A C

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