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Areas Related to Circles
Question
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Construct a circle whose radius is equal to 4 cm. Let P be a point whose distance from its centre is 6 cm. Construct two tangents to it from P.

Answer

Steps of Construction :

(i) Take a point O in the plane of the paper and draw a circle of radius 4 cm.
(ii) Mark a point P at a distance of 6 cm from the centre O and join OP.
(iii)    Bisect the line segment OP. Let the point of bisection be M.
(iv)    Taking M as centre and OM as radius, draw a circle to intersect the given circle at the points T and T’.
(v) Join PT and PT’ to gel the required tangents.

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Some More Questions From Areas Related to Circles Chapter

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

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Let ABC be a right angle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.  

Draw a line segment of length 7.6 cm and divide it in the ratio 3 : 5.

Divide the given line segment AB of length 6 cm internally in the ratio 3 : 4.

Divide a line segment 11 cm in the ratio of 2 : 5 (a) internally (b) externally.