Math  /  Geometry

QuestionPoint PP represents which point of concurrency? a. centroid b. incenter c. orthocenter d. circuncenter

Studdy Solution

STEP 1

What is this asking? Which special point on a triangle is the center of a circle *inside* the triangle and touching all its sides? Watch out! Don't mix up the different kinds of triangle centers; they have similar-sounding names!

STEP 2

1. Define Incenter
2. Analyze the Diagram
3. Identify the Point

STEP 3

Hey everyone!
Let's talk about the **incenter** of a triangle.
It's the point where the *angle bisectors* of a triangle meet.
Remember, an *angle bisector* is a line that cuts an angle perfectly in half!

STEP 4

The really cool thing about the incenter is that it's the center of the **inscribed circle**, which is a circle that fits *perfectly* inside the triangle, just *kissing* each side.

STEP 5

Take a close look at the diagram!
We see a triangle ABCABC with a circle *snuggled* inside.
Notice how the circle *touches* each side of the triangle.

STEP 6

That means the circle in the diagram is the **inscribed circle** of the triangle!
And what do we know about the center of the inscribed circle?
It's the **incenter**!

STEP 7

The problem tells us that point PP is the center of the circle.
Since we've figured out that this circle is the **inscribed circle**, we know that PP must be the **incenter**!

STEP 8

The answer is (b) incenter.
Point PP is the incenter of triangle ABCABC.

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