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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

Given: PT炉is tangent to 鈯�Oat T;TS炉鈯�PO炉

Complete the following statements.

a. TS is the geometric mean between ? and ?

b. TO is the geometric mean between ? and ?

c. If OS=6 and SP=24,TS=? and TP=?

In exercises 8-13 find the angle or the arc named.

EHF铃�

Name three radii of 鈯�o.

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

In exercises 8-13 find the angle or the arc named.

GHE铃�
See all solutions

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