The triangle ABC has sides AB = 137, AC = 241 an BC = 200. There is a point D, on BC, such that both incircles of triangles ABD and ACD touch AD at the same point E. What is the length of CD?
A. 152
B. 174
C. 179
D. 183
E. 197
[spoiler]https://gmatmaths.com/[/spoiler]
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
touch AD at the same point E
This topic has expert replies
-
sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
-
anshumishra
- Legendary Member
- Posts: 543
- Joined: Tue Jun 15, 2010 7:01 pm
- Thanked: 147 times
- Followed by:3 members
Please refer to the diagram below :sanju09 wrote:The triangle ABC has sides AB = 137, AC = 241 an BC = 200. There is a point D, on BC, such that both incircles of triangles ABD and ACD touch AD at the same point E. What is the length of CD?
A. 152
B. 174
C. 179
D. 183
E. 197
[spoiler]https://gmatmaths.com/[/spoiler]
This is based on the theory : Two tangents can always be drawn to a circle from any point outside the circle, and these tangents are equal in length
x+y = 137 --- 1
x+z = 241 ---- 2
y+z+2w = 200 --- 3
Need to find : CD = CF"+DF" = w+z = ?
Add (1) and (2) =>2x+y+z = 137+241 = 378 --- 4
Subtract (1) and (2) => z-y = 241-137 = 104 ---- 5
Add (3) and (5) => y+z+2w+z-y = 200+104
=> 2(z+w) = 304
=> z+w = 152, A
Thanks
Anshu
(Every mistake is a lesson learned )
Anshu
(Every mistake is a lesson learned )
-
Night reader
- Legendary Member
- Posts: 1337
- Joined: Sat Dec 27, 2008 6:29 pm
- Thanked: 127 times
- Followed by:10 members
x^2-y^2=200^2 - 137^2;
x+y=241
(x-y)(x+y)=(200-137)(200+137)
x+y=241
x-y=200-137
x+y=241, 2x=304, x=152 --> CD=152
answer A
sanju09 wrote:The triangle ABC has sides AB = 137, AC = 241 an BC = 200. There is a point D, on BC, such that both incircles of triangles ABD and ACD touch AD at the same point E. What is the length of CD?
A. 152
B. 174
C. 179
D. 183
E. 197
[spoiler]https://gmatmaths.com/[/spoiler]
- Attachments
-
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
