Math Problem Statement
Solution
To solve for the area of triangle , we will follow these steps:
Step 1: Identify given values
- (this is the radius of the circle)
- (another radius of the circle)
- is a tangent at point to the circle, which means that .
Step 2: Use the Pythagorean theorem
Since is a right-angled triangle at , we can apply the Pythagorean theorem to find the length of .
Substituting the values of and :
Step 3: Calculate the area of
The area of a right-angled triangle is given by:
Here, is the base and is the height.
Thus, the area of is approximately 45.96 cm².
Would you like more details or have any questions?
Here are some related questions:
- How do you calculate the hypotenuse in a right triangle?
- How does the tangent property of circles help in solving geometry problems?
- What is the significance of the right angle in triangle area calculations?
- Can you generalize the method to find the area of any right triangle?
- How do you use the Pythagorean theorem in three-dimensional geometry?
Tip: Always remember that a tangent to a circle forms a right angle with the radius at the point of tangency.
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Math Problem Analysis
Mathematical Concepts
Geometry
Right Triangle
Circle Theorems
Formulas
Pythagorean theorem: a² + b² = c²
Area of a triangle: (1/2) × base × height
Theorems
Pythagorean Theorem
Tangent-Radius Theorem (Tangent forms a right angle with the radius)
Suitable Grade Level
Grades 8-10
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