# Geometry Problem 1542: Unraveling a Geometric Puzzle with a Circumscribed
Right Triangle and Square to the Same Circle for School and College

A right triangle ABC with a right angle at B is circumscribed to a circle with center O, and a square BDEF is also circumscribed to the same circle. Point D lies on line BC, point F lies on line AB, and the lines FE and DE intersect line AC at points M and N respectively. Given that AM = 16 and MN = 6, we need to determine the length of NC.

**Problem 1542**

Triangle, square meet,

Circle's embrace holds their form,

Minds solve geometry.

## Lines and Shadows: Exploring Problem 1542 with Machu Picchu as the Backdrop

## Discover Even More: See Also...

### Problem 1543

### Problem 1541

### Problem 1540

### Problem 1539

### Problem 1538

### Problem 1537

### Read more, explore further

Geometry Problems

Open Problems

Visual Index

All Problems

Circle

Triangle

Right Triangle

Square

Angle Bisector

Circle Inscribed in a Square

Incircle

Similarity

View or Post a solution

### Search our site with Google: