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Chapter 9: Q18. (page 337)

Circles Pand Qhave radii 6 and 2 and are tangent to each other. Find length of their common external tangent AB.炉

Short Answer

Expert verified

The required length is,

AB=45.

Step by step solution

01

Step 1. Given information.

Circles Pand Qhave radii 6 and 2 and are tangent to each other.

Given figure,

02

Step 2. Concept used.

There are two circles whose radius is 6 and 2 respectively.

Joint APand BQ.

Note that APand BQare radius, then

AP=6BQ=2

03

Step 3. Draw the construction.

Joint PQand joint OBand make a parallel line to PQ. ThenOPQB will be a rectangle.

In the rectangle OPQBopposite sides are equal.

OB=PQ=4OP=QB=2.................(1)

Then,

AP=AO+OP6=AO+2AO=6鈭�2AO=4.............(1)

The distance PQis,

PQ=radius1+radius2=6+2=8

From (1), OB=PQand PQ=8

This implies that OB=8

Note that 螖AOBis a right-angled triangle.

04

Step 4. Use Pythagoras theorem.

AB2=OA2+OB2=42+82=16+64=80

Take positive square root to get,

AB=80=45

Therefore, the required length is, AB=45.

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Most popular questions from this chapter

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.

Prove theorem 9.2

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.

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.

Why TK炉 is not a chord of 鈯�o.
See all solutions

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