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Question

Draw a circle of any radius. From a point outside the circle, draw tangents to the circle inclined at 45 to each other. [4 MARKS]


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Solution

Construction : 3 Marks
Steps of construction : 1 Mark



Steps of construction :

Note: The quadrilateral PMON has the sum of all its angles as 360 but we know 3 angles angle M and angle N are 90 and angle P is 45. So, angle O has to be 135.

1. Construct a circle of any convenient radius.

2. Draw a radius OM and create MON = 135.

3. At M and N, construct two tangents.

4. Let these tangents intersect at P.

5. MPN = 45



So, to draw the given tangent, draw a tangent from any point on the circle. Join it to a centre and draw another radius inclined to the first at an angle of 135 . Draw another tangent from this point on the circle. The point at which these 2 tangents intersect is the point P outside the circle from which the tangents drawn to the circle are inclined at an angle of 45 .


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