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Chapter 9: Q5. (page 335)

The diagram below shows tangent lines and circles. Find PD.

Short Answer

Expert verified

The value of PD=8路2

Step by step solution

01

Step 1. Given information.

The figure here given is,

02

Step 2. Consider circle I.

In the given figure, AP and BP are given as the tangents to the circle.

Use the fact that if BP,鈥�AP are tangents to a circle from an external point to a circle then BP=鈥�AP,

BP=AP=8.2

03

Step 3. Consider circle II.

CP and BP are tangents to the circle.

As it is known that tangents drawn from any point external to the circle onto the same circle are equal,

CP=BP=8.2

04

Step 4. Consider circle III.

PD and PC are tangents to the circle.

As tangents drawn from an external point to a circle are equal,

Therefore, PD=PC=8.2

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Most popular questions from this chapter

Find the radius of the circle inscribed in the triangle.

鈯�Q and 鈯�R are congruent circles the intersect at C andD. CD炉 is called the common chord of the circles.

  1. What kind of quadrilateral is QDRC? Why?
  2. CD炉Must be the perpendicular bisector of 鈯�Q. Why?
  3. If QC=17 and QR=30, find CD.

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

a. Draw a three large circles and inscribe a different shaped quadrilateral ABCDin each.

b. Use a protractor to measure all the angles.

c. Compute m鈭�A+m鈭�C and m鈭�B+m鈭�D..

d. What is the relationship between opposite angles of an inscribed quadrilateral?
See all solutions

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