Question

5. If AB = 8 cm, AC=6 cm, BC=9 cm, AD is the bisector of angle A, then BD:DC= .................​

Answer 1

Answer:

8:9

Step-by-step explanation:

AB:AC=BD:DC

AB=8cm and AC=9cm

therefore,BD:DC=8:9

Answer 2

Answer: $\frac{32}{49}$

Step-by-step explanation:

• In a ΔABC, AB=8 cm, AC=6 cm and BC=9 cm.
• AD bisets ∠A.
• Let BD=x cm, so DC=(9-x) cm.
• In ΔADB,

         $AD=\sqrt{8^{2}-x^{2} }$

And in ΔADC,

         $AD=\sqrt{9^{2} -(81+x^{2} -18x)}$

                = $\sqrt{18x-x^{2} }$

Equating both the values of AD we get,

            18x=64

         ⇒ x=$\frac{32}{9}$

∴ DC= $9-\frac{32}{9}$

       = $\frac{49}{9}$

Ratio of BD and DC= $\frac{\frac{32}{9} }{\frac{49}{9} }$

                                = $\frac{32}{49}$

• Hence, the required ratio is  $\frac{32}{49}$.

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