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.
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.
Related Questions
Using ruler and compasses only :
(i) Construct a triangle ABC with the following data :
BC = 7 cm, AB = 5 cm and ∠ABC = 45°.
(ii) Draw the inscribed circle to △ABC drawn in part (i).
Draw a circle of radius 3 cm. Mark its centre as C and mark a point P such that CP = 7 cm. Using ruler and compasses only, construct two tangents from P to the circle.
Using ruler and compasses only, construct an equilateral triangle of height 4 cm and draw its circumcircle.
Using ruler and compasses only, construct a triangle ABC having given c = 6 cm, b = 7 cm and ∠A = 30°. Measure side a. Draw the circumcircle of the triangle.