Construction Of Tangents To Circle

Construction of Tangents to Circle Example 1: Draw a circle of radius 2 cm. Take any point P on it and draw a tangent to the circle at this point. Solution:

Steps of construction 1. Draw a circle of radius 2 cm 2. Mark its centre as O. 3. Mark a point P on the circle and join OP. 4. Make an angle of 90o at P. Now QPR is the required tangent. Example 2: Draw a circle of radius 3 cm. From a point P, 8 cm away from its centre draw two tangents. Solution:

Steps of construction 1. Draw a line segment PO = 8 cm 2. At draw a circle of radius 3 cm 3. Bisect PO 4. From the mid point of PO, that is Q, draw a circle passing through O and P which cuts the circle O at R and S. 5. Join PR and PS. Now PR and PS are the two required tangents to the circle. Example 3: Draw a line segment of length 6 cm. With its ends as centers draw a circle of radii 2 cm and 3 cm. From the centers of these circles draw tangents to each other. Solution:

Steps of construction 1. Draw a line segment AB of length 7 cm 2. With A and B as centers radii 2 cm and 3 cm respectively draw circles. 3. Draw the right bisector PQ of line segment AB, cutting AB at O. 4. With O as centre and OB as radius draw a circle, intersecting the two circles at T1 and T2 and S1 and S 2 respectively. 5. Join BT1 and BT2 and AS1 and AS2 . These are the required tangents. Example 4: Using the bottom of a circular tumbler, draw a circle. From a point P outside the circle, draw to tangents to the circle. Solution:

Steps of construction 1. Draw a two chords AB and BC of circle O. 2. Bisect them. Let they meet at O. 3. Join OP and bisect it 4. From mid point PO, which is Q, draw a circle intersecting circle O at T1 and T2 . 5. Join PT1 and PT2 These are the required tangents ***************************************************