Two circles of radii 8 cm and 5 cm with their centres A and B respectively touch externally as shown in the figure. Calculate the length of direct common tangent PQ

Open in App

Solution

Draw a line parallel to PQ from point B such that it cuts AP at M.

It is given that AP = 8 cm and BQ = 5 cm.

Here, we need to find the length of PQ.

AM = AP – PM = AP – BQ = 8 cm – 5 cm = 3 cm

Since the two circles touch each other externally, the distance between their centers is equal to sum of their radii.

AB = 8 cm + 5 cm = 13 cm

Applying Pythagoras theorem in right ΔMAB, we have:

PQ = BM = 12.64

Hence, the length of the common tangent is 12.64 cm.

Suggest Corrections

Similar questions

Two circles of radii 8 cm and 5 cm with their centres A and B respectively touch externally as shown in the figure. Calculate the length of direct common tangent PQ

Q. Two circles of radii

18 c m

and

8 c m

touch externally. The length of a direct common tangent to the two circles is

Q. Tangents

P A

and

P B

are drawn from an external point

P

to two concentric circle with centre

O

and radii

8 c m

and

5 c m

respectively, as shown in figure. If

A P = 15 c m,

then find the length of

B P .

Q. The ratio of two circles is

r_{1}

and

r_{2}

. If the two circles touch externally, then the length of their direct common tangent is __________.

In the figure, B and C are the centres of the 2 circles with radii 9 cm and 3 cm respectively. Also, PQ is the transverse common tangent.
Find the length of PQ, if the centres of circles are 15 cm apart.

Join BYJU'S Learning Program