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 length of the tangents.
Answer
(i) 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.
Hence, above is the required circle.
(ii) Steps of construction :
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.
Related Questions
Construct a triangle ABC in which base BC = 5.5 cm, AB = 6 cm and ∠ABC = 120°.
(i) Construct a circle circumscribing the triangle ABC.
(ii) Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.
Using a ruler and compasses only :
(i) Construct a triangle ABC with the following data :
AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°.
(ii) In same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.
(iii) Measure ∠BCP.
Construct a triangle ABC in which AB = 5 cm, BC = 6.8 cm and median AD = 4.4 cm. Draw incircle of this triangle.
Using a ruler and a compass, construct a triangle ABC in which AB = 7 cm, ∠CAB = 60° and AC = 5 cm. Construct the locus of :
(i) points equidistant from AB and AC.
(ii) points equidistant from BA and BC.
Hence construct a circle touching the three sides of the triangle internally.