Solving a Geometry Problem: Inscribed Half Circle and Triangle Relationships

  • Thread starter Anzas
  • Start date
  • Tags
    Geometry
In summary, it is proven that ED equals the radius of the circle inscribed in triangle ABC, by showing that DEFG forms a rectangle and the length of ED is equal to the radius of the half circle.
  • #1
Anzas
87
0
http://members.lycos.co.uk/anzas/geo/problem.gif

in triangle ABC a half circle is inscribed.
the circle's diameter KL, is parallel to side AB
CD is the height of the triangle ABC
CD = 14 cm
AB = 10 cm
prove that ED equals to the circles radii
 
Physics news on Phys.org
  • #2
Is there not only one radius ?
Besides, if you don't have to calculate the radius, this is pretty straightforward.
 
  • #3
in the drawing there are no radii's only the diameter KL
also the center of the circle is not given.
im pretty sure that what's needed to be proven is that ED = KL/2
i just don't know how...
 
  • #4
ED equal the circle radius because it is just the distance from the diameter to the parallel tangent to the circle. I don't need to calculate the radius here. Maybe you tricked me to get the answer...
 
  • #5
no i didnt trick you that might be one way to prove it but there should be a proof a bit more complex...
 
  • #6
Doubtlessly. Do you need to actually compute the radius ?
 
  • #7
no as the question states i need to prove that ED equals to the circles radii
(in a diffrent way from the one you described)
 
  • #8
Anzas said:
no as the question states i need to prove that ED equals to the circles radii
(in a diffrent way from the one you described)

Ok, humanino was right though...

since CD is the height of the triangle then CD and AB are perpendicular

which means that angle EDB = 90degrees

As well We know that a line tangent to a circle is perpendicular to the radius

In the drawing FG is perpendicular to AB so FGD = 90 degrees

as well FG and ED is perpendicular to KL since KL is parallel to AB

DEL and GFK = 90 degrees

so this proves that DEFG forms a rectangle with ED and FG being opposite sides thus being equal. FG equals the radius of the half circle, thus ED = radius of circle
 

Attachments

  • problem1.gif
    problem1.gif
    3.8 KB · Views: 448
Last edited:

What is a problem in geometry?

A problem in geometry is a mathematical question or puzzle that involves shapes, sizes, and measurements. It requires the use of geometric principles and formulas to solve.

What are some common types of problems in geometry?

Some common types of problems in geometry include finding the perimeter, area, or volume of a shape, identifying congruent or similar shapes, and solving for unknown angles and sides in geometric figures.

What skills are necessary to solve problems in geometry?

To solve problems in geometry, one must have a strong understanding of geometric concepts such as angles, lines, shapes, and measurements. They must also be able to apply geometric formulas and use mathematical reasoning to solve the problem.

How can I improve my problem-solving skills in geometry?

To improve problem-solving skills in geometry, it is important to practice regularly and familiarize oneself with different types of problems. It can also be helpful to break down the problem into smaller, more manageable steps and to use visual aids such as diagrams or drawings.

Are there real-life applications for solving problems in geometry?

Yes, there are many real-life applications for solving problems in geometry. For example, architects use geometry to design buildings, engineers use it to construct bridges and roads, and artists use it to create visually appealing compositions. Understanding geometry can also help in everyday tasks such as measuring and designing furniture or navigating using maps and directions.

Similar threads

  • Computing and Technology
Replies
13
Views
2K
Replies
1
Views
2K
Replies
6
Views
783
Replies
13
Views
2K
  • General Math
Replies
2
Views
2K
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
11
Views
2K
Replies
1
Views
2K
  • Precalculus Mathematics Homework Help
Replies
4
Views
3K
  • Precalculus Mathematics Homework Help
Replies
14
Views
9K
Back
Top