Question

Construct a circle of radius 7cm. From a point 10 cm away from its centre, draw tangents to the circle. [4 MARKS]

Answer 1

Construction : 3 Marks
Steps of construction : 1 Mark

Steps of construction :

1. Draw a circle with 'O' as centre and radius 7 cm.
2. Mark a point P outside the circle such that OP = 10cm.
3. Draw a line segment from P to the centre of the circle O and bisect it. Let it be at a point, say M.
4. With M as centre and PM as radius draw a circle. Let this circle intersect the initial circle at points X and Y
5. Join PX and PY.
6. Since PO is the diameter of the new circle, $\angle X$ and $\angle Y$ are ${90}^{\circ }$ ( Angles in a semicircle)
But OX and OY are radii of the circle.
7. Any line that makes a right angle with the radius and touches the circle at only 1 point is a tangent to a circle.
8. Hence PX and PY have to be tangents to the circle.