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Chapter 9: Q14. (page 342)

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�.)

Short Answer

Expert verified

(a)

The final answer is

Arc length WX鈮�arc length XY.

Step by step solution

01

Step 1. Given information:

WZ炉 is a diameter of circle and OX炉鈭�ZY炉

02

Step 2. Concept used:

We use basic geometric and angle concept

03

Step 3. Applying the concept:

First let us draw OY炉in the given figure.

Then OY炉and OZ炉becomes radii of the circles 鈬�OY炉=OZ炉

Let 鈭�WOX=x掳, since OX炉鈥�||ZY炉鈥�then 鈭�OZY鈥�鈥�=x掳and also 螖鈥�OZYis isosceles triangles as OY炉=OZ炉then 鈭�OYZ鈥�鈥�=x掳

From 螖鈥�OZY, we have 鈥�鈭�OZY+鈭�ZYO+鈭�YOZ=1800

鈬�x鈭�+x鈭�+鈭�ZOY=180鈭�鈬�鈭�ZOY=180鈭�鈭�2x鈭�

Also from straight line WZ炉, we have 鈥�鈭�WOX+鈭�XOY+鈭�ZOY=1800

鈬�x鈭�+鈭�XOY+180鈭�鈭�2x鈭�=180鈭�鈬�鈭�XOY鈭�x鈭�=180鈭�180鈭�鈭�XOY=x鈭�

Thus, 鈭�WOX=x掳=鈭�XOY

鈬�Arcs made by same angle in a circle are congruent.

Hence, Arc length WX鈥�鈥�鈮�arc lengthXY.

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Most popular questions from this chapter

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).

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

Is there a theorem about spheres related to the theorem in Exercise 12? If so, state the theorem.

Plane Z passes through the center of sphere Q.

  1. Explain why QR=QS=QT.
  2. Explain why the intersection of the plane and the sphere is a circle. (The intersection of a sphere with any plane passing through the center of the sphere is called a great circle of the sphere).

Find AB.In Exercise 3,CB炉 is tangent to 鈯�A.
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