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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.

Constructions

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Answer

(i) Steps of construction :

  1. Draw a line segment AB = 5 cm.

  2. With A as center cut an arc of 3 cm on AB to obtain C.

  3. With A as center and radius = 2.5 cm draw an arc.

  4. With C as center and radius = 2.5 cm draw an arc cutting the previous arc and mark the point O.

  5. With O as center and radius = 2.5 cm draw a circle.

Hence, above is the required circle.

(ii) Steps of construction :

  1. Join OB.

  2. Draw the perpendicular bisector of OB, let it meet OB at point M.

  3. With M as center and radius equal to OM, draw a circle to cut the previous circle at points P and Q.

  4. Join PB and QB. Hence, PB and QB are required tangents. Measure PB and QB.

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. Constructions, Concise Mathematics Solutions ICSE Class 10.

On measuring PB = QB = 3.2 cm.

Hence, length of each tangent = 3.2 cm.

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