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The image contains a problem related to geometry, specifically involving a triangle and some calculations. Below is a summary of the content:

### Problem Description:
1. A triangle \( \triangle ABC \) is situated on the coordinate plane with the following details:
   - \( A \) is the origin \((0,0)\).
   - \( B \) is at \( (18,0) \), meaning it's on the x-axis.
   - \( C \) is a point such that its y-coordinate \( y \) is 15.
   
2. There are several questions regarding the properties of this triangle:
   1. Calculate the length of \( AB \).
   2. Calculate the length of \( BC \) using the given coordinates.
   3. Determine the slope of the line \( AC \) if point \( C \) has a certain x-coordinate.
   4. Find the equation of the line passing through point \( A \) and perpendicular to \( BC \).
   5. Determine the area of \( \triangle ABC \).

Would you like a detailed step-by-step solution to each of these problems, or do you have specific questions about any part of the problem?

#### Here are 5 related questions you might consider next:
1. How do you find the coordinates of a point \( C \) in a triangle when given specific conditions?
2. What is the formula to calculate the distance between two points in a coordinate plane?
3. How can you determine if a line is perpendicular to another in the coordinate plane?
4. How do you calculate the area of a triangle given the coordinates of its vertices?
5. What is the relationship between the slope of a line and the angle it makes with the x-axis?

**Tip:** When solving problems involving coordinates, always ensure the units are consistent and double-check your calculations for accuracy.

There is a circle with a center at (0,0) and a radius of 10 units. On this circle, a chord AB is located with points A and B at coordinates (0,10) and (8,6), respectively. The problem asks for: 1. The equation of the perpendicular bisector of AB; 2. The coordinates of the center of the circle that circumscribes triangle ABC, where C is a point on the coordinate plane; 3. The length of the tangent drawn from point P(4,2) to the circle; 4. Determining whether a given line segment passes through the circle's center.

Solve complex coordinate geometry problems involving a circle with a radius of 10 units, a chord, and points on the coordinate plane. Learn how to find the equation of a perpendicular bisector, determine the center of a circumscribing circle, and calculate tangent lengths. Suitable for Grades 10-12.

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