Find the Max of $PC$ in $\triangle ABC$

  • Context: MHB 
  • Thread starter Thread starter Albert1
  • Start date Start date
  • Tags Tags
    Max pc
Click For Summary
SUMMARY

The discussion centers on finding the maximum length of segment $PC$ in an equilateral triangle $\triangle ABC$ where the lengths of segments $PA$ and $PB$ are given as 2 and 3, respectively. The problem is framed within the context of triangle geometry, specifically focusing on the relationship between the distances from point $P$ to the vertices of the triangle. The solution involves applying geometric principles to derive the maximum value of $PC$ based on the constraints provided.

PREREQUISITES
  • Understanding of equilateral triangles and their properties
  • Knowledge of geometric distance relationships
  • Familiarity with triangle inequality theorem
  • Basic skills in coordinate geometry
NEXT STEPS
  • Study the properties of equilateral triangles and their centroid
  • Explore the triangle inequality theorem in depth
  • Learn about geometric optimization techniques
  • Investigate coordinate geometry methods for distance calculations
USEFUL FOR

Mathematicians, geometry enthusiasts, students studying triangle properties, and anyone interested in geometric optimization problems.

Albert1
Messages
1,221
Reaction score
0
$\triangle ABC$ with $AB=BC=CA$
if another point $P$ and $PA=2, \,\, PB=3$
please find :$max(PC)$
 
Mathematics news on Phys.org
Albert said:
$\triangle ABC$ with $AB=BC=CA$ if another point $P$ and $PA=2, \,\, PB=3$ please find :$max(PC)$

my solution:
 

Attachments

  • MAX(PC)..jpg
    MAX(PC)..jpg
    17.5 KB · Views: 119

Similar threads

MHB Proving $\angle ABC$ is Acute: Inside the Triangle $ABC$
  • · Replies 4 ·
Replies
4
Views
1K
MHB What are the angles of an isosceles triangle with a specific ratio?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Proving $PA+PB+PC\geq MA+MB+MC$ in $\triangle ABC$
  • · Replies 2 ·
Replies
2
Views
2K
MHB Can You Find the Angle in This Isosceles Triangle Problem?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Proving Equality of Angles in an Acute Triangle
  • · Replies 4 ·
Replies
4
Views
1K
MHB Please find the side length of an equilateral triangle
  • · Replies 3 ·
Replies
3
Views
2K
MHB Area of Triangle ABC Given Dimensions
  • · Replies 5 ·
Replies
5
Views
2K
MHB Area of Triangle ABC: Find the Solution
  • · Replies 2 ·
Replies
2
Views
2K
High School A triangle problem: Prove that |AC|+|AB|=|PR|+|PQ| given some constraints
  • · Replies 13 ·
Replies
13
Views
3K
MHB Find the scale factor of triangle ABC to triangle DEF
  • · Replies 5 ·
Replies
5
Views
3K