Construction of tangents to a circle and their properties

Construct circle with radius = r

Length of tangents from an external points are equal.

Sum of the angle at the centre of circle and at external point is supplementary.

Draw a circle with centre and radius

Take a point p outside of it.

Join the points o and p

Find mid-point of segment op

Draw a circle with centre c and passing through o and p

Mark the intersecting points of two circles as Q and R

Draw lines passing through PQ and PR which are the required tangents.

Find angles PRO and OQP

Find angles QPR and ROQ

Draw a line from C perpendicular to OP.

Join OQ and OR

Draw segments PQ and PR

Move slider or point P to verify the properties:-

Prepared by - Roshan Lakra
Copy Right - CC by SA

radius = 4 (slider from 1 to 6, step 1)
O = (1.9, 1.44)
c = Circle(O, radius)
P = (8.76, 1.52)
f = Segment(O, P)
C = Midpoint(f)
d = Circle(C, P)
R, Q = Intersect(d, c)
g = Line(Q, P)
h = Line(R, P)
i = Segment(Q, P)
j = Segment(R, P)
distanceEB = Distance(Q, P)
distanceBD = Distance(P, R)
TextBD: Name[P] + (Name[R]) + " = " + distanceBD
distanceBE = Distance(P, Q)
TextBE: Name[P] + (Name[Q]) + " = " + distanceBE
k = OrthogonalLine(Q, i)
l = OrthogonalLine(R, j)
m = Segment(Q, O)
n = Segment(R, O)
α = Angle(O, Q, P)
β = Angle(P, R, O)
text3: "Length of tangent PQ=" + j + ""
text2: "Length of tangent PR=" + i + ""
γ = Angle(R, O, Q)
δ = Angle(Q, P, R)
sumofoppositeangles: γ + δ
text4: "Sum of opposite angles= " + γ + "+" + δ + "=" + sumofoppositeangles + ""
p = OrthogonalLine(C, f)
a = true
b = true
e = true
o = true
q = true
r = true
s = true
t = true
u = true
w = true
v = true
a_1 = true