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]
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]
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∘ .
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∘ .
