triangle

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Tue Feb 09, 2010 1:04 pm

In a triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with center B) is drawn. If the circle cuts AB and BC at P and Q respectively, then AP : QC is equal to

1 : 1
3 : 2
4 : 1
3 : 8
1 : 3

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Source: Beat The GMAT — Problem Solving | Tue Feb 09, 2010 1:04 pm

girish3131: Master | Next Rank: 500 Posts; Posts: 194; Joined: Thu Jan 14, 2010 5:18 am; Thanked: 2 times

by girish3131 » Wed Feb 10, 2010 11:16 pm

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Wed Feb 10, 2010 11:36 pm

girish3131 wrote:E

Girish will you provide your solution. how did you reached to the answer E[spoiler] i.e. 1:3.[/spoiler]

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girish3131: Master | Next Rank: 500 Posts; Posts: 194; Joined: Thu Jan 14, 2010 5:18 am; Thanked: 2 times

by girish3131 » Wed Feb 10, 2010 11:52 pm

Plz provide OA..

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Wed Feb 10, 2010 11:56 pm

I am attaching diagram of this question so that you can try and solve problem easily.

[spoiler]OA is 3:8 i.e. D[/spoiler]

Last edited by shashank.ism on Wed Feb 10, 2010 11:57 pm, edited 1 time in total.

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Wed Feb 10, 2010 11:56 pm

shashank.ism wrote:In a triangle ABC, AB = 6, BC = 8 and AC = 10. A perpendicular dropped from B, meets the side AC at D. A circle of radius BD (with center B) is drawn. If the circle cuts AB and BC at P and Q respectively, then AP : QC is equal to

1 : 1
3 : 2
4 : 1
3 : 8
1 : 3

Acc. to the ques, 1/2 Ã— BC Ã— AB = 1/2 Ã— BD Ã— AC
Or, 6 Ã— 8 = BD Ã— 10. Thus BD = 4.8. Therefore, BP = BQ = 4.8.
So, AP = AB - BP = 6 - 4.8 = 1.2 and CQ = BC - BQ = 8 - 4.8 = 3.2.
Thus, [spoiler]AP : CQ = 1.2 : 3.2 = 3 : 8.Hence, D.[/spoiler]

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djkvakin: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Sat Oct 03, 2009 1:13 pm; Thanked: 11 times

by djkvakin » Thu Feb 11, 2010 11:37 am

Also, from the diagram, it is evident, that AP is smaller than QC, therefore in our answer choice we should see the first part of the ratio smaller than the second. This eliminates A, B, and C. So you could focus on 2 other choices.

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sars72: Master | Next Rank: 500 Posts; Posts: 241; Joined: Wed Jan 27, 2010 10:10 pmFollowed by: 2 members; Location: Chennai; Thanked: 23 times; GMAT Score:690

by sars72 » Thu Feb 11, 2010 11:44 am

djkvakin wrote:Also, from the diagram, it is evident, that AP is smaller than QC, therefore in our answer choice we should see the first part of the ratio smaller than the second. This eliminates A, B, and C. So you could focus on 2 other choices.

I don't think you can assume this unless it is explicitly stated that the diagram is drawn to scale.

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djkvakin: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Sat Oct 03, 2009 1:13 pm; Thanked: 11 times

by djkvakin » Thu Feb 11, 2010 1:41 pm

sars72 wrote:
djkvakin wrote:Also, from the diagram, it is evident, that AP is smaller than QC, therefore in our answer choice we should see the first part of the ratio smaller than the second. This eliminates A, B, and C. So you could focus on 2 other choices.
I don't think you can assume this unless it is explicitly stated that the diagram is drawn to scale.

In this case it's safe to assume that because QC is part of BC, and is defined as a longer leg than BA, when both BA and BQ=to radius of the circle.

In general, I do agree with you that unless it's explicitly stated that the picture is drawn to scale, it's not safe to assume anything. In this case, I didn't assume that based on the drawing, but rather analysis above.

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Thu Feb 18, 2010 11:15 am

sars72 wrote:
djkvakin wrote:Also, from the diagram, it is evident, that AP is smaller than QC, therefore in our answer choice we should see the first part of the ratio smaller than the second. This eliminates A, B, and C. So you could focus on 2 other choices.
I don't think you can assume this unless it is explicitly stated that the diagram is drawn to scale.

I do agree with sars 72 that unless given clearly,we should not assume the figure is drawn to scale.
Sometimes the figure can just be used as a trap to defy our illusion.

I think it is better to spend a bit more time and go by the formal approach:-
1/2 X BC X AB = 1/2 X BD X AC

Alternatively,we see 6,8,10 is a right angled triangle.Thus we have a 30-60-90 triangle.
So,using the sine and cosine of 30(degree) and 60(degree) we can also solve the question.

I would prefer the above 2 approaches rather than doing the question by eye estimation.
Also,by elimination also we are let with 2 answer choices.So,ultimately we have to solve the question formally.

It takes time and effort to explain, so if my comment helped you please press Thanks button

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