## Saturday, March 11, 2023

### Geometry Problem 1525: Unveiling the Secrets of an Equilateral Triangle in Right Triangle Geometry: Finding the Midpoint Distance between Segments. Difficulty Level: High School.

Geometry Problem 1525. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

More Details

To post a solution to this problem click Comment underneath the post, or click into the line that says, “Enter Comment.” Type what you want to say and press Publish to post your solution.

1. https://photos.app.goo.gl/Qt4wWUDARG6fzTrbA

2. Why the sketch is deleted

3. I'm sorry to hear that your sketch was deleted from the blog. there may have been a technical issue that led to the deletion. I have just re-sent your post to the blog. Thank you.

1. Let P be the mid-point of CD

In Triangles BMN & CPN,
< MBN = < PCN (= A - 30)
BN = NC (since N is the circumcenter of right triangle ABC)
BM = MP (since Triangle DPM is equilateral)
So Triangles BMN & CPN are congruent SAS

Now using the midpoint theorem in Triangle ACD,
MN = NP = AD/2 = 6/2 = 3

Sumith Peiris
Moratuwa
Sri Lanka