Construct a tangent to a circle of radius 5 cm from a point on the concentric circle of radius
7 cm and measure its length.
Answers
(1)Draw two concentric circle C
1
and C
2
with common center
0 and radius 4cm and 6cm
(2) Take a point P on the outer circle C
2
and join OP.
(3) Draw the bisector of OP which bisect OP at M'.
(4) Taking M' as center and OM' as radius draw a dotted circle which
cut the inner circle C
1
at two point M and P.
(5) Join PM and PP'. Thus, PM and PP' are required tangent.
On measuring PM and PP'.
PM=PP
′
=4.4cm
Bycalculation:
InΔOMP,∠PMO=90
0
PM
2
=OP
2
−OM
2
(bypythagorastheorem)
PM
2
=(6)
2
−(4)
2
=36−16=20
PM
2
=20cm
PM=
20
=4.4cm
Hence,
thelengthofthetangentis4.4cm
STEPS OF CONSTRUCTION:
1.Draw two concentric circles C1 and C2 with common Centre O and radius 5cm 7 cm.
2. Take any point P on outer circle C2 and join OP.
3. Draw the bisector of OP which bisect OP at M’.
4. Taking M’ as centre and OM’ as radius draw a dotted circle with cuts the inner circle C1 at two points M & P’.
5.Join PM & PP’ . Thus PM & PP’ are Required tangents.
➠ On measuring PM & PP’
PM = PP’ = 4.9cm
➞ By calculation:
In ∆ OMP, ∠PMO= 90°
PM² = OP² - OM²
[ by Pythagoras theorem]
➛ PM² = (7)² -(5)²
➛ PM² = 49 - 25
➛ PM² = 24
➛PM² = 24cm
➛ PM = √24
➨ PM² = 4.9 cm
Hence, the length of the tangents is 4.9cm.
