Draw a line $A B = 5 c m$ . Mark a point $C$ on $A B$ such that $A C = 3 c m$ . using a ruler and a compass only construct :
(i) a circle of radius $2.5 c m$ 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 .

Open in App

Solution

steps for construction

· draw AB=5cm
· with A as centre cut an arc of 3cm on AB and mark it C
· with A as centre and radius 2.5cm, draw an arc and mark it O
· with O as centre and radius 2.5cm, draw a circle so that points A and C lie on the circle formed
· join OB
· draw perpendicular bisector of OB to obtain mid point of OB, M
· with M as the centre and radius equal to OM, draw a circle to cut the previous circle at point P and Q
· join PB and QB, PB and QB are required tangents to the given circle from exterior point B

$Q B = P B = 3 c m$

The length of the tangents is $3 c m$

Suggest Corrections

Similar questions

Draw a circle of radius 3 cm and mark two chords AB and AC of the circle of lengths 4 cm and 5 cm respectively, using ruler and compasses only. Then the locus of points, inside the circle, that are equidistant from A and C, passes through the centre of the circle.

Q. Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2.5 cm. Construct tangents to each circle from the centre of the other circle.

Q. Draw a right triangle