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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

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.

a. m鈭�AOB=90掳

a. Given:WZ炉is a diameter of 鈯�o;OX炉鈭�ZY炉

Prove: WX铃�鈮�XY铃�.

(Hint: draw OY铃�.)

RS炉 and TU炉are common internal tangents to the circles. If RZ=4路7 and ZU=7路3, Find RS and TU.

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?
  2. Write an argument that justifies your answer to part (a).

a. Draw a circle. Place points A,B, and C on it in such positions that

\[mAB铃�+mBC铃�\]does not equal

b. Does your example in part (a) contradict Postulate 16?
See all solutions

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