Mathematics, 16.07.2019 15:40 amanramesh2004

The figure shows △abc . bd is the angle bisector of ∠abc . what is ad ? enter your answer in the box as a fraction. units

Answers

From angle bisector theorem, we know that:

$\dfrac{|AD|}{|DC|}=\dfrac{|BA|}{|BC|}\\\\\\\dfrac{|AD|}{|DC|}=\dfrac{8}{10}=\dfrac{4}{5}$

Moreover:

|AD|+|DC|=6

so:

and

$\dfrac{|AD|}{|DC|}=\dfrac{4}{5}\\\\\\\dfrac{|AD|}{6-|AD|}=\dfrac{4}{5}\qquad\qquad\text{cross multiplying}\\\\\\ 5\cdot|AD|=4\cdot\big(6-|AD|\big)\\\\5\cdot|AD|=24-4\cdot|AD|\\\\5\cdot|AD|+4\cdot|AD|=24\\\\9\cdot|AD|=24\qquad|:9\\\\\\|AD|=\dfrac{24}{9}=\boxed{\dfrac{8}{3}}$

Answer from: Quest

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Answer from: Quest

a negative exponent is translated as follows:

$a^{-m} = \dfrac{1}{a^m}$

so, we have

$\left(5^{-1}+3^{-1}+2^{-1}\right)^{-1} = \left(\dfrac{1}{5}+\dfrac{1}{3}+\dfrac{1}{2}\right)^{-1} = \left(\dfrac{6+10+15}{30}\right)^{-1}=\left(\dfrac{31}{30}\right)^{-1}=\dfrac{30}{31}$

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The figure shows △abc . bd is the angle bisector of ∠abc . what is ad ? enter your answer in the b...