Question

Draw a circle of radius 4cm from a point 6cm away to the circle construct a pair of tangents to the circle measure their length

Answer 1

Draw the circle with compass and extend r 6cm

Answer 2

Answer:

Step-by-step explanation:

Radius of the circle = OC=4 cm

Straight distance of the point B from circle = CB = 6 cm

therefore,

The distance between the point B and center of the circle $OB=4+6=10\text{ cm}$

Draw a tangent AB

Now in $\Delta OAB,\text{ }\angle OAB=90^\circ$

therefore,

$OB^{2}=OA^{2}+AB^{2}\\\\\Rightarrow100^{2}=4^{2}+AB^{2}\\\\\Rightarrow100=16+AB^{2}\\\\\Rightarrow{AB}^{2}=100-16\\\\\Rightarrow{AB}^{2}=86\\\\\Rightarrow{AB}=\sqrt{86}\\\\\Rightarrow{AB}=9.27\text{ cm}$

Therefore

The length of the tangent = 9.27 cm