# TANGENCY III

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TANGENT TO A CIRCLE FROM A GIVEN POINT OUTSIDE IT

Procedure

Given
R= 30 and OP= 65

1. Draw the given circle with centre at O and locate the given point P.
2. Join PO and bisect it at X.
3. Centre at X, radius XO, draw a semicircle to cut the given circle at q.
4. Join QP to get the required tangent.

TANGENTS AND ARCS/ CURVES

A. TO DRAW ARCS TO TOUCH TWP CIRCLES OF UNEQUAL RADII ABOVE THE CIRCLES (EXTERNAL)

GIVEN
R= 70
r1= 20
r2= 30
Distance between centres O1 and O2= 70

Procedure

1. Draw the given circles with centres at O1 and O2.
2. Centre at O1, radius R-r1, describe an arc.
3. Centre at O2, radius R-r2, cut the arc at O.
4. Centre at O, radius R, draw the required arc( circle) to include the other two.

B. TO DRAW ARCS TO TOUCH TWO CIRCLES OF UNEQUAL RADII BELOW THE CIRCLES ( INTERNAL)

GIVEN
R=50
r1=20
r2=30
Distance between centres O1 and O2 =60

Procedure

1. Draw the given circles with centres at O1 and O2.
2. Centre at O1, radius R+r1, describe an arc.
3. Centre at O2, radius R+r2, cut the arc at O.
4. Centre at O, radius R, draw the required circle(arc).

C. TRANSVERSE CIRCLES

GIVEN
R= 70
r1= 20
r2= 30
Distance between centres O1 and O2=70

Procedure

1. Draw the given circles centres at O1 and O2.
2. Centre at O1, radius R+r1, describe an arc.
3. Centre at O2, radius R-r2, cut the arc at O.
4. Centre at O, radius R, draw the transverse circle(arc).

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