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Prove that the circle drawn on any on...

Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base. Given: A ` A B C` in which `A B=A C` and a circle is drawn by taking `A B` as diameter which intersects the side `B C` of triangle at `D` To Prove: `B D=D C` Construction : Join `A D`

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Proof: `angleADB=90^*`
(Angles in a semi-circle is a right angle)
`angleABC+angleADC=180^*`
`angleADC=90^*`
In `triangleABD` and `triangleACD`
`AB=AC` (given)
`angleADB=angleADC` (each `90^*`)
`AD=AD` (common)
...
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RD SHARMA-CIRCLE -All Questions
  1. BC is a chord with centre O. A is a point on an arc BC . Pr...

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  2. BC is a chord with centre O. A is a point on an arc BC . Pr...

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  3. Prove that the circle drawn on any one of the equal sides of an iso...

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  4. In Figure, A ,B , C are three points on a circle such that the angles ...

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  5. In Figure, O is the center of the circle and the measure of arc ABC is...

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  6. In Figure, O is the center of the circle. The angle subtended by the a...

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  7. In Figure, find m /PQB where O is the center of the circle

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  8. Two circle intersect in Aa n dBa n dA Ca n dA D are respectively the d...

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  9. Two circles are drawn with sides A B ,A C of a triangle A B C as diame...

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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. In the figure, P is the centre of the circle. Prove that: /X P Z=2\...

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  12. In a circle with centre O , chords A B\ a n d\ C D intersect ins...

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  13. C is a point on the minor arc AB of the circle, with centre ...

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  14. In Figure, chord E D is parallel to the diameter A C of the circ...

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

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

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

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

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

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