Question

20. In the figure, centre of the large circle is A and its
radius 9cm .
Centre of the small circle is B and its
radius is 4cm. Two circles touches at c. Find the
the common
in tangent
PQ.

Answer 1

Answer:

The common tangent QR is equal to PS

Triangle OSP is right angled triangle. (from given figure)

PSQR is a rectangle. (All four interior angles of quadrilateral PSQR are right angles. Since tangent is perpendicular to radius at point of contact; and PS is also perpendicular to OQ)

OS=OP−SP=8−4=4cm

From the Pythagorean Theorem we have

OP

2

=OS

2

+SP

2

now SP=

OP

2

−OS

2

SP=

12

2

−4

2

...... [OS=4cm and OP=8+4=12cm]

SP=

128

SP=8

2

cm

also the opposite sides of a rectangle are equal .

Therefore length of commen tangent QR=8

2

cm