Another problem involving a triangle and its bisector. Would you like to try solving it?

Liudmyla Hetmanenko @Liudmyla-Hetmanenko

19 December 2023 1 9K Report

In triangle ABC, the angle bisector AD of angle BAC is drawn.

AC+CD=m.

AB-BD=n.

Find AD

Sergey E. Gladun

b:=AC, c:=AB, x:=BD, y:=CD, l=AD; b+y=m, c-x=n; l^2=bc-xy;

mn=(b+y)(c-x)=bc-xy+cy-bx=bc-xy.

Then l=sqrt(mn).

Badges
Science topic

More Liudmyla Hetmanenko's questions See All

A new interesting geometry problem. Can you find the measure of angle?

In the isosceles triangle ABC (AC=AB), the angle at the vertex is 20°. Point D is chosen on the side AB such that AD=BC. Find the measure of angle CDB.

23 June 2024 7,541 8 View

The problem at hand concerns the application of the "II Lagrange's formula". Would you like to try solving it?

In triangle ABC, the bisector AL₁ is drawn. Points O₁, O₂, O are the centers of the circles circumscribed around triangles ACL₁, ABL₁, ABC, respectively. The radii are denoted as R₁, R₂, R for...

12 June 2024 7,596 1 View

A new interesting problem. Would you like to try solving it?

Consider a circle of radius R with center O. Two other circles are internally tangent to this circle and intersect at points A and B. Find the sum of the radii of the other two circles, given...

29 May 2024 9,788 1 View

There's a new beautiful geometric problem. Would you like to try solving it?

Two circles with radii R and r touch externally at point A. Through point B, which belongs to the larger circle, a tangent to the smaller circle is drawn to point C. Find the length of the...

22 May 2024 4,420 1 View

Find the distance from point K to side BC. Do you have any ideas on how to solve it?

The circle touches AB and AC the lateral sides of the isosceles triangle ABC at the vertices B and C (Fig. 1). On the arc of this circle, which lies inside this triangle, there is a point K so...

11 May 2024 7,124 6 View

Original Geometry Problem.Can you solve it?

In a right-angled triangle ABC (∠C=90°), the height CD equals to h is drawn. The points M and N are chosen on the continuation of AB such that NA=AD and DB=BM (Fig. 1). Find the distance from...

29 April 2024 8,913 3 View

I have a new interesting geometric problem. Do you have any ideas on how to solve it?

In a right-angled triangle ABC (∠C=90°), the height CD equal to h is drawn. The points M and N are the midpoints of the segments BD and AD. Find the distance from the point C to the orthocenter...

06 April 2024 5,232 6 View

I have a new geometric problem. Do you have any ideas on how to solve it?

Point X belongs to the circle inscribed in the equilateral triangle ABC (see Figure 1). Lines parallel to the sides of the triangle are drawn through point X. The areas of the formed triangles...

30 March 2024 5,406 5 View

Dear colleagues, I present to you another elegant geometry problem. Who can solve this problem?

A circle is inscribed in triangle ABC (AC=AB). The point of heights’ intersection (orthocenter) (Fig. 1) belongs to this circle. Find the angles of triangle ABC (Fig. 2).

19 March 2024 1,162 8 View

Original Geometry Problem.Can you solve it?

In triangle ABC (with angle C = 90 degrees), the legs are equal to 5 and 7. From vertex C, segment CD is drawn (with D belonging to side BA) such that circles inscribed in triangles CAD and CBD...

26 February 2024 5,358 30 View

What is the difference between mathematical R^4 space and physical 4D unit space?

We assume that the difference is huge and that it is not possible to compare the two spaces. The R^4 mathematical space considers time as an external controller and the space itself is immobile in...

10 August 2024 6,678 14 View

Which Scopus Journal provides the most affordable fees?

"PUBLISHING IN A SCOPUS JOURNAL" Researchers are now at a cross road. The critical need to publish in a Scopus or ISI, etc journal is ever vital. Journal Publication fees must be submitted....

10 August 2024 8,621 1 View

Seeking Advice on Viability and Execution of Undergraduate Thesis Topic?

Hello everyone, I am currently developing a thesis proposal and would appreciate your input on its viability and how to effectively carry it out. My proposed topic is: "Does the perceived threat...

10 August 2024 8,992 0 View

Who will be moral responsible for the death of thousands of people in the event of an earthquake?

Who will bear moral responsibility for the deaths of thousands of people in the event of an earthquake? Weeks and months remain before the onset of strong earthquakes that bring death to...

08 August 2024 6,134 12 View

May members post flyers about opportunities to present at a conference? If so, where to post?

May members post flyers about opportunities to present at a conferehttps://veraeducation.com/nce? If so, where to post for the Virginia Educational Research Association? https://veraeducation.com/

08 August 2024 4,585 1 View

Are there any instruments for studying time similar to the way it is in space?

There are a huge number of methods for studying objects in space, according to the senses (and not only). Mechanical, thermal, optical, acoustic, electrical, magnetic, based on particle beams,...

06 August 2024 7,102 0 View

In the case of a wound l recurrence after radical breast cancer and sentinel lymph node biopsy. Are the sentinel lymph node procedure recommended?

In the case of a wound l recurrence after radical breast cancer and sentinel lymph node biopsy. Are the sentinel lymph node procedure recommended? If no axillary lymph node dissection was not...

05 August 2024 8,056 1 View

Regarding a model for simulating battery charge and discharge, what do you consider to be high fidelity?

Regarding a model for simulating battery charge and discharge, what do you consider to be high fidelity? What is the acceptable percentage of error (regardless of the metric)? Could you suggest...

03 August 2024 5,358 0 View

Interested in a SCOPUS collaboration?

Hi RG family. My team and I are working on some SCOPUS publications and we need co-authors who are willing and capable of undertaking both qualitative and quantitative-based studies. The scope...

02 August 2024 7,843 0 View

Interested in a SCOPUS collaboration?

Hi RG family. My team and I are working on some SCOPUS publications and we need co-authors who are willing and capable of undertaking both qualitative and quantitative-based studies. The scope of...

02 August 2024 8,572 0 View