Mathematics
Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only construct:
(i) A circle of radius 2.5 cm passing through A and C.
(ii) Construct two tangents to the circle from the external point B.
Measure and record the lengths of the tangents.
Constructions
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Answer
Steps of construction :
Draw a line segment AB = 5 cm.
With A as center cut an arc of 3 cm on AB to obtain C.
With A as center and radius = 2.5 cm draw an arc.
With C as center and radius = 2.5 cm draw an arc cutting the previous arc and mark the point O.
With O as center and radius = 2.5 cm draw a circle.
Join OB.
Draw the perpendicular bisector of OB, let it meet OB at point M.
With M as center and radius equal to OM, draw a circle to cut the previous circle at points P and Q.
Join PB and QB. Hence, PB and QB are required tangents.
Measure PB and QB.
On measuring, PB = QB = 3.2 cm.
Hence, length of each tangent = 3.2 cm.
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