1.

Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Drew tangents to the circle from these two points P and Q.

Answer»

Solution :Given, two points P and Q on the diameter of a circle with rasius 3 cm. and OP = OQ = 7 cm
We have to construct the tangents to the circle from the given points P and Q.
Steps of Construction :
1. DRAW a circle of radius 3 cm with centre at O.
2. Produce its diameter on both sides and take points P and Q on diameter such that OP - OQ = 7 cm,
3. BISECT OP and OQ. Let E and F be the mid-points of OP and OQ, respectively.
4. Take E as centre and OE as radius draw a circle which interect the given circle (0,3) at two points M and N.
Again, taking F as centre and OF as radius draw a circle which intersect the given circle (0,3) at two points P' and Q'
5. Join PM, PN, QP' and QQ'. These are the required tangents from P and Q to the given, circle (0,3).
Justifiction : Join OM and ON. The `angleOMP` is the angle lies in the semi-circle and therefore `angleOMP=90^(@).` Since, OM is radium of the circle. So, MP has to be tangent to the circle. Similarly PN, QP' and QQ' are also tangents to the given circle.


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