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Bisectors of angles A, B and C of a tria...

Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that angles of the triangle are `90^@-A/2,90^@-B/2` and `90^@-C/2` respectively.

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MODERN PUBLICATION-CIRCLES-EXERCISE
  1. Bisectors of angles A, B and C of a triangle ABC intersect its circumc...

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  2. The radius of a circle is 8 cm and the length of its chords is 12 cm. ...

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  3. Find the length of a chord which is at a distance of 24 cm from the ce...

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  4. A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the...

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  5. Find the length of a chord which is at a distance of 24 cm from the ce...

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  6. PQ and RS are two parallel chords of a circle whose centre is O and ra...

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  7. PQ and RS are two parallel chords of a circle whose centre is O and ra...

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  8. AB and CD are two chords of a circle such that AB = 6 cm, CD = 12 cm a...

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  9. Two parallel chords of lengths 30 cm and 16 cm are drawn on the opposi...

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  10. In an equilateral triangle, prove that centroid and circumcentre coinc...

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  11. Two chords PQ and RS of a circle are parallel to each other and AB is ...

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  12. In fig., two circles with centres O, O' touch externally at a point A....

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  13. Prove that the right-bisector of a chord of a circle bisects the corre...

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  14. Two chords AB and AC of a circle are equal. Prove that the centre of t...

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  15. Two equal chords AB and CD of a circle C(O,r) when produced meet at a ...

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  16. Two equal chords AB and CD of a circle C(O,r) when produced meet at a ...

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  17. If a diameter of a cirlce bisects each of the chords of the circle, pr...

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  18. Prove that the perpendicular at the point of contact to the tangent to...

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  19. Diameter is the largest chord of the circle. (True/False)

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  20. PQ and RQ are chords of a circle equidistant from the centre. Prove th...

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  21. In given Fig. , AD = AE and D and E are points on BC, such that BD = ...

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