Draw a circle of radius 5cm. Draw any line through the centre of the circle. Draw a tangent to the circle making an angle of 45° with the line. What is the length of the tangent?

Consider a rough figure as shown CB is tangent and centre of the circle is A. CA is a line passing through the centre

∠BCA = 45° …given

∠CBA = 90° …radius is perpendicular to the tangent

Consider ΔABC

⇒ ∠ABC + ∠ACB + ∠BAC = 180° …sum of angles of triangle

⇒ 90° + 45° + ∠BAC = 180°

⇒ 135° + ∠BAC = 180°

⇒ ∠BAC = 45°

Now let us construct

Step1: Take distance 5 cm in compass and draw a circle with centre A and draw a line passing through A

Step2: Using protractor draw the line at 45° to the line drawn in step1 from point A intersecting circle at B

Step3: Using protractor draw a line perpendicular to AB from point B because the radius is perpendicular to the tangent. Mark the intersection of this line with a line passing through the centre as C hence CB is the required tangent at 45°

Measure the length CB with a scale which is the length of the tangent

CB = 5 cm length of tangent is 5 cm