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Triangle Properties and Theorems

Triangle Properties and Theorems

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Practice Problem

Hard

Created by

Thomas White

FREE Resource

In this video, the problem of finding the area of a right triangle with an inscribed circle is tackled. The video begins with an introduction to the problem and the setup of the triangle. The two tangent theorem is explained and applied to determine congruent line segments. The dimensions of the triangle are calculated using given lengths and theorems. A quadratic equation is derived and solved to find the radius of the inscribed circle. Finally, the area of the triangle is calculated using the derived values, resulting in an area of 135 square units.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the length of line segment CD in the given problem?

24 units

15 units

9 units

12 units

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which theorem states that two tangent segments from the same external point to a circle are congruent?

Circle Theorem

Congruent Segments Theorem

Two Tangent Theorem

Pythagorean Theorem

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If AD is 15 units, what is the length of AE according to the Two Tangent Theorem?

15 units

12 units

24 units

9 units

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the total length of the longest leg AC in the triangle?

15 units

18 units

24 units

9 units

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What formula is used to calculate the dimensions of the right triangle?

Area formula

Pythagorean theorem

Quadratic formula

Two Tangent Theorem

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the quadratic equation derived to find the radius of the circle?

r² + 24r - 135 = 0

r² + 48r - 270 = 0

r² + 30r - 225 = 0

r² + 18r - 81 = 0

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the base of the triangle ABC after substituting the radius?

15 + 3 * sqrt(31)

3 * sqrt(31) - 3

9 + 3 * sqrt(31)

3 * sqrt(31) + 3

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