CONSTRUCTIONS
Rough Figure
O
P
Q
7 cm
7 cm
Q. Draw a circle of radius 3cm.
Take two points P and Q on
one of its extended diameters
each at a distance of 7cm
from its centre. Draw tangents
to the circle from these two
points P and Q.
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N
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Ex-13.2 (Q.3)
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H
7 cm
7 cm
A
B
C
D
Draw a circle of radius of 3cm and centre O
Locate points P and Q such that OP = OQ = 7cm
Draw perpendicular bisector of seg OP
O as centre and radius more than half of OP, draw arcs on either sides
Now P as centre and with the same radius, cut previously drawn arcs
Draw line EF intersecting OP at M
Now M as centre and radius = OM or MP
Draw a circle intersecting previously drawn circle at A and B
Draw ray PA and PB
Q as centre and radius more than half of OQ, draw arcs on either sides
Draw perpendicular bisector of seg OQ
Now O as centre and with the same radius, cut previously drawn arcs
Draw line GH
intersecting OQ at N
Now N as centre and radius = ON or NQ
Draw a circle intersecting previously drawn circle at C and D
Draw ray QC and QD
PA and PB are required tangents from external point P
QC and QD are required tangents from external point Q
3 cm
Q. Draw a circle of radius 3cm. Take two points P and Q on one of its extended diameters
each at a distance of 7cm from its centre. Draw tangents to the circle from these two
points P and Q.
Justification :
Join OA then ∠OAP is an angle in a semicircle.
∴
∠OAP = 90°
∴
line PA ⊥ radius OA.
∴
PA has to be a tangent to circle
[A line ⊥ to radius to a circle
at its outer end is a tangent]
Similarly, we can show that PB, QC and QD
are the tangents.
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M
P
Q
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7 cm
7 cm