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Chapter 9: Q23. (page 337)

Find the radius of the circle inscribed in the triangle.

Short Answer

Expert verified

The radius of the circle is, 22.

Step by step solution

01

Step 1. Given information.

The given figure is,

02

Step 2. Concept used.

In any triangle,

s=a+b+c2where a and b are c the sides of the triangle.

Here,

a=12b=12c=8

03

Step 3. Put the values to find s.

s=12+12+82s=322s=16

Let the radius of circle ber.

04

Step 4. Formula used.

The radius of the circle inscribed in the triangle is given by the formula,

r2=s鈭�as鈭�bs鈭�csr2=16鈭�1216鈭�1216鈭�816r2=4脳4脳816r=8r=22

05

Step 5. Neglect negative sign. 

Since, length is positive,

So, neglecting the negative value.

Therefore, the radius of the circle is, 22.

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Most popular questions from this chapter

JK炉 is tangent to 鈯�P and 鈯�Q.

JK=?

Given: Two tangents circles; EF炉 is a common external tangent;

GH炉 is the common internal tangent.

a. Discover and prove something interesting about point G.

b. Discover and prove something interesting about 鈭�EHF.

For each exercise draw 鈯�O with radius 12. Then draw radii OA炉 and to OB炉 form an angle with the measure named. Find the length of AB炉.

d. m鈭�AOB=120掳

Draw two points A & B and several circles that pass through A and B. Locate the centers of these circles. On the basis of your experiment, complete the following statement:

The centers of all circles passing through A and B lie on ______.

Write an argument to support your statement.

Draw a diagram similar to the one shown, but much larger. Carefully draw the perpendicular bisectors of AB炉 and BC炉.

  1. The perpendicular bisect in a point. Where does that point to be?
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