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Question

Draw ¯¯¯¯¯¯¯¯PQ, where PQ=10cm. Draw circle (P,4) and (Q,3). Draw tangents to each circle from the centre of the other circle. Write points of construction.

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Solution

Data: Draw ¯¯¯¯¯¯¯¯PQ such that PQ=10cm. Draw circle (P,4) and (Q,3)
To Construct: From the centre of each circle, tangents are to be drawn to the circle.
Steps of Construction:
(i) Draw ¯¯¯¯¯¯¯¯PQ such that PQ=10cm. Draw circle (P,4) and (Q,3).
(ii) Obtain the midpoint M of ¯¯¯¯¯¯¯¯PQ by constructing its perpendicular bisector.
(iii) Draw (M,MP) to intersect (Q,3) at S andT and (P,4) at X and Y.
(iv) Draw ¯¯¯¯¯¯¯¯¯QX and ¯¯¯¯¯¯¯¯¯QY as well as ¯¯¯¯¯¯¯¯PS and ¯¯¯¯¯¯¯¯PT.
(v) Thus ¯¯¯¯¯¯¯¯¯QX and ¯¯¯¯¯¯¯¯¯QY are the tangents from Q to (P,4) and ¯¯¯¯¯¯¯¯PS and ¯¯¯¯¯¯¯¯PT are the tangents from P to (Q,3)
666654_626383_ans_234bd80f6c84494bb97f956d5ce81147.png

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