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Lapatulllka [165]
3 years ago
11

The center of the inscribed circle of Triangle ABC is point , and the center of the circumscribed circle of Triagnle ABC is poin

t .

Mathematics
1 answer:
quester [9]3 years ago
5 0

Answer:

Part A: The center of The inscribed circle is the point S

Part B: The center of The circumscribed circle is the point P

Step-by-step explanation:

Part A: Find the center of The inscribed circle of ΔABC

The inscribed circle will touch each of the three sides of the triangle in exactly one point,

The center of the inscribed circle is the point of intersection between the angle bisectors of the triangle.

<u>So, </u>According to the previous definition:

A₁A₂ and B₁B₂ are the angle bisectors of ∠A and ∠B

So, the inter section between them is the center of <u>The inscribed circle</u>

<u>So, the center of The inscribed circle is the point S</u>

=====================================================

Part B: Find the center of The circumscribed circle of ΔABC

The circumscribed circle is the circle that passes through all three vertices of the triangle.

The center of the circumscribed circle is the point of intersection between the perpendicular bisectors of the sides.

<u>So,</u> According to the previous definition:

P₁P₂ and Q₁Q₂ are the perpendicular bisectors of AB and BC

So, the inter section between them is the center of <u>The circumscribed circle</u>

<u>So, the center of The circumscribed circle is the point P</u>

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Answer:

x = 7.5

Step-by-step explanation:

Since the midsegment and the third segment of the triangle are parallel to each other, therefore,

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2 years ago
How many times does 5 go into 100
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3 years ago
Of the students in Rosalie's dance class, 29 out of 59 have participated in dance class before. About how many of her students h
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2 years ago
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Marques drops a plate from a height of 5 feet. When will the plate hit the ground?
nadya68 [22]

Answer:

<u>Option A. about 1 seconds</u>

Step-by-step explanation:

Let the initial speed u and the final speed v

Time t , distance s and acceleration of gravity g

The equation of motion are:

v = u + gt            ⇒(1)

s = ut + 0.5 gt²   ⇒(2)

v² = u² + 2gs      ⇒(3)

Marques drops a plate from a height of 5 feet.

So, u = 0 , s = 5 ft , g = 9.8 m/sec²

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s = ut + 0.5 gt²

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3 years ago
Professor Easy's final examination has 9 true-false questions followed by 3 multiple-choice questions. In each of the multiple-c
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Answer:    2⁹5³ = 64,000

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There are 9 questions with 2 options (true or false) = 2⁹

There are 3 multiple questions with 5 options = 5³

true/false questions AND multiple choice questions

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