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Question
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:
- A circle of radius 2.5 cm, passing through A and C.
- Construct two tangents to the circle from the external point B. Measure and record the length of the tangents.
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Solution
Steps for construction:
- Draw AB = 5 cm using a ruler.
- With A as the centre cut an arc of 3 cm on AB to obtain C.
- With A as the centre and radius 2.5 cm, draw an arc above AB.
- With same radius and C as the centre draw an arc to cut the previous arc and mark the intersection as O.
- With O as the centre and radius 2.5 cm, draw a circle so that points A and C lie on the circle formed.
- Join OB.
- Draw the perpendicular bisector of OB to obtain the mid-point of OB, M.
- With the M as the centre and radius equal to OM, draw a circle to cut the previous circle at points P and Q.
- Join PB and QB. PB and QB are the required tangents to the given circle from exterior point B.
QB = PB = 3 cm
That is, length of the tangents is 3 cm.
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