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As the figure shows AD = 3, BD = 5 and BC = 9. Moreover, point I is the incenter of triangle ABC. What is the length o

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As the figure shows AD = 3, BD = 5 and BC = 9. Moreover, point I is the incenter of triangle ABC. What is the length o

by Max@Math Revolution » Mon Feb 03, 2020 12:28 am
[GMAT math practice question]

As the figure shows AD = 3, BD = 5 and BC = 9. Moreover, point I is the incenter of triangle ABC. What is the length of AC?
2.3ps.png
A. 3
B. 4
C. 5
D. 6
E. 7
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Re: As the figure shows AD = 3, BD = 5 and BC = 9. Moreover, point I is the incenter of triangle ABC. What is the leng

by Pyunika » Tue Feb 04, 2020 12:45 am
Since I is the in center BI,Di and EI will be perpendicular.
And DI=EI=r
So using Pythagoras we can say BD=BE= 5cm
thus EC = 4 cm
By applying the same logic as above CF=EC= 4cm and AD=AF= 3cm
This AC= AF+FC =7cm
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Re: As the figure shows AD = 3, BD = 5 and BC = 9. Moreover, point I is the incenter of triangle ABC. What is the leng

by Max@Math Revolution » Wed Feb 05, 2020 5:17 pm
=>

Since AD = AF, we have AF = 3.
Since BC = 9 and BD = 5, we have FC = EC = BC – BE = BC – BD = 9 – 5 = 4.

Then we have AC = AF + FC = 3 + 4 = 7.

Therefore, E is the answer.
Answer: E
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