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The Unknown Side (Posted on 2002-07-01)

ABC is a triangle:

Angle A < 90.

D is a point on BC such that BD = DC.

M is a point on BC such that AM is perpendicular to BC.

AD = 10,

BC = 12 and

MC = 11
find the length of AC.

See The Solution Submitted by Dulanjana

Rating: 2.9091 (11 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Puzzle Resolution

| Comment 14 of 16 |

(In reply to answer by K Sengupta)

MB = BC-MC = 12-11 = 1
BC = 12, and so: BD = DC =6
Thus, DM = DB - MB = 6-1=5

Accordingly, AM = V(10^2 - 5^2) = V(75)

But MC = 11, and so:
AC = sqrt(AM^2 + MC^2)
= sqrt(75+121)= sqrt(196) = 14

Edited on March 24, 2022, 8:43 pm

Posted by K Sengupta on 2007-06-15 12:21:11

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