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In A B C ,C=60^0a n dB=45^0dot Line joi...

In ` A B C ,C=60^0a n dB=45^0dot` Line joining vertex A of triangle and its circumcenter `(O)` meets the side `B CinD` Find the ratio `B D : D C` Find the ratio `A O : O D`

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To solve the problem, we need to find the ratios \( BD : DC \) and \( AO : OD \) in triangle \( ABC \) with given angles. ### Step 1: Determine the angles of triangle \( ABC \) Given: - \( C = 60^\circ \) - \( B = 45^\circ \) ...
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CENGAGE ENGLISH-PROPERTIES AND SOLUTIONS OF TRIANGLE-Illustration
  1. In A B C ,a , ca n dA are given and b1,b2 are two values of the third...

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  2. O is the circumcenter of A B Ca n dR1, R2, R3 are respectively, the r...

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  3. In A B C ,C=60^0a n dB=45^0dot Line joining vertex A of triangle and ...

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  4. The diameters of the circumcirle of triangle ABC drawn from A,B and C ...

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  5. Find the lengths of chords of the circumcircle of triangle ABC, made b...

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  6. Let A B C be a triangle with /B=90^0 . Let AD be the bisector of /A wi...

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  7. If the distances of the vertices of a triangle =ABC from the points of...

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  8. If x , ya n dz are the distances of incenter from the vertices of the ...

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  9. Prove that cosA+cosB+cosC=1+r/R

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  10. Prove that ("a c o s"A+b cosB+ccosC)/(a+b+c)=r/Rdot

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  11. Incircle of A B C touches the sides BC, CA and AB at D, E and F, resp...

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  12. In an acute angled triangle A B C , a semicircle with radius ra is con...

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  13. Let the incircle with center I of A B C touch sides BC, CA and AB at ...

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  14. In A B C , the bisector of the angle A meets the side BC at D andthe ...

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  15. Let I be the incetre of ΔABC having inradius r. Al, BI and Ci intersec...

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  16. In A B C , the three bisectors of the angle A, B and C are extended t...

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  17. Given a right triangle with /A =90^@. Let M be the mid-point of BC. If...

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  18. Prove that the distance between the circumcenter and the incenter of ...

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  19. Prove that acosA+bcosB+ccosClt=sdot

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  20. If Delta is the area of a triangle with side lengths a, b, c, then s...

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