Mathematics
Draw a line AQ = 7 cm. Mark a point P on AQ such that AP = 4 cm. Using ruler and compasses only, construct :
(i) a circle with AP as diameter
(ii) two tangents to the above circle from the point Q.
Constructions
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Answer
(i) Steps of construction :
Draw a line segment AQ = 7 cm. Mark the point as AP = 4cm.
Draw perpendicular bisector of AP let it meet AP at O. Such that AO = OP = radius of circle with centre O..
With O as centre and radius AO draw a circle. This is the circle with AP as diameter.
(ii) Steps of construction :
Join OQ.
Draw perpendicular bisector of OQ to meet OQ at M.
With M as centre and OM (or MQ) as radius, draw a circle. Let this circle intersect the circle with O as centre at points C and D.
Join QC and QD.
Hence, QC and QD are tangents to the circle with centre O from the point Q.
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