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Chapter 9: Q17. (page 337)

JK炉 is tangent to 鈯�P and 鈯�Q.

JK=?

Short Answer

Expert verified

The given quadrilateral JPQK must be a Trapezium.

Step by step solution

01

Step 1. Given information.

The figure here given is,

JK is tangent to the circle with centers P and Q.

02

Step 2. Draw the construction in figure.

The measures of the sides are,

PQ=17QK=3PD=3PJ=11

OT is required to find the measures of sides JDand JK.

Now,

PJ鈯�JK And QK鈯�JK

Joint PJand QKand make a line parallel to PQ that is DK.

Then, it implies that,

PQ=DK=17 ........(1)

To find DK,

03

Step 3. Concept used.

Triangle JKD is a right angle triangle so one can use Pythagoras Theorem,

The measures of sides in this right angle triangle are,

DK=17JD=11鈥�3=8

04

Step 4. Use Pythagoras Theorem as follows.

DK虏=JK虏+JD虏17虏=JK虏+8虏289=JK虏+64JK虏=289鈥�64=225

Take positive square to get,

JK=15

So, the required length is JK=15.

In quadrilateral PQJK, sum one pair of adjacent angle is 180掳.

Therefore, it can be concluded that the opposite sides is parallel.

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Most popular questions from this chapter

Name a secant of the sphere and a chord of the sphere.

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.

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.

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

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�.)
See all solutions

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