Question

Construct a direct common tangent to two circles of radii 4 cm and 2 cm whose centres are 8 cm apart. Measure and verify the length of the tangent.

Answer 1

$PQ=\sqrt{d^2-(r_1-r_2{)}^2}PQ=\sqrt{8^2-2^2}PQ=7.75cm$

• Draw a line segment $AB=15cm$. Draw circle $C1$ with radius $4cm$ and centre as $A$. Draw circle $C2$ with radius $2cm$ and centre $B$
• Draw circle $C3$ with radius $(R_1-R_2=4-2=2cm$ and centre $A$. $B$ is the external point to circle $C3$. Draw perpendicular bisector of $AB$ and mark its midpoint $M$
• With $M$ as centre and $AM$ as radius construct a circle $C4$
• $C4$ cuts $C3$ at two points $E$ and $F$. Join $AE$ and $AF$
• Extend $AE$ to meet $C1$ at $P$ and $AF$ to meet $C1$ at $R$
• Draw $BQ\parallel AP$ and $BS\parallel AR$
• Join $PQ$ and $RS$. $PQ$ and $RS$ are required direct tangents.