Construct Trig ABC: BC=a, BD=b, BA=c

Your Name]In summary, to construct a triangle ABC with side lengths a, b, and c with BD as the bisector of angle ABC, draw a line segment BC with length a, then draw a line segment BD with length b from point B. Mark a point D on BD with length b, and then draw a circle with center D and radius c intersecting BC at point A. Connect points A and C to complete the triangle. This satisfies the given conditions and ensures that BD is the bisector of angle ABC. Thank you.
  • #1
solakis1
422
0
Given a,b,c construct a trigon ABC with :BC=a,BD=b,BA=c. BD is the bisector of the angle ABC
 
Mathematics news on Phys.org
  • #2

Thank you for your question. Constructing a triangle with given side lengths and a bisector can be done using a few steps:

1. Draw a line segment BC with length a. This will be the base of the triangle.

2. From point B, draw a line segment BD with length b. This will be the angle bisector of angle ABC.

3. On the line segment BD, mark a point D such that BD = b.

4. With center D and radius c, draw a circle intersecting the line segment BC at point A.

5. Connect points A and C to complete the triangle ABC.

This construction satisfies the given conditions of BC = a, BD = b, and BA = c, and also ensures that BD is the bisector of angle ABC.

I hope this helps. Please let me know if you have any further questions.
 

FAQ: Construct Trig ABC: BC=a, BD=b, BA=c

1. What is the first step in constructing a triangle with given side lengths?

The first step is to draw a line segment of length BC (a) and label its endpoints as B and C.

2. Can any point be chosen for point D in the construction of this triangle?

No, point D must be chosen on the line segment BC such that BD is equal to the given length b.

3. How many solutions are possible for this construction?

There can be either two solutions or no solution, depending on the given values of a, b, and c.

4. What is the second step in constructing this triangle?

The second step is to draw a circle with center at point B and radius equal to the given length c.

5. Can this triangle be constructed using only a straightedge?

No, this construction requires both a straightedge and a compass to draw the circle.

Similar threads

MHB Prove $(CD)^2=(BD)^2+\dfrac{(BC)^2(AD)}{AB}$ for Isosceles Trigon ABC
Replies
1
Views
827
MHB Find $\angle B$ for Triangle $ABC$ with Bisectors $AD,BE$
Replies
1
Views
969
MHB Simplify a+b+c+d+2(ab+ac+ad+bc+bd+cd)+4(abc+abd+acd+bcd)+8(abcd)
Replies
3
Views
2K
B A triangle problem: Prove that |AC|+|AB|=|PR|+|PQ| given some constraints
Replies
13
Views
2K
MHB Triangular Relations: Proving (AD)^2+(DE)^2+(AE)^2= \frac{2}{3}(BC)^2
Replies
1
Views
1K
MHB Proving Equality of Angles in an Acute Triangle
Replies
4
Views
972
MHB How to Evaluate $\dfrac{a^5+b^5+c^5-1}{abc}$ Given $ab+bc+ca=0$ and $abc\ne 0$?
Replies
1
Views
817
MHB Find Length of Side in Right Triangle w/ 45°, 90°, and 45° Angle
Replies
2
Views
1K
MHB Triangle Equality Proof: $\frac{a}{b}=1+\sqrt{2\left(\frac{c}{b}\right)^2-1}$
Replies
1
Views
1K
MHB Prove Geometric Sequence with $(a,b,c)$
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top