Draw $\overline{ XY }$ of length $11\, cm$. Draw $\odot( X, 4\, cm )$ and $\odot( Y, 3\, cm)$. From the centre of each circle,draw tangents to the other circle. Write the steps of construction.
(N/A) Steps of construction:
$1$. Draw a line segment $\overline{ XY } = 11\, cm$.
$2$. Draw a circle with center $X$ and radius $4\, cm$,and another circle with center $Y$ and radius $3\, cm$.
$3$. Find the midpoint $M$ of $\overline{ XY }$ by drawing the perpendicular bisector of $\overline{ XY }$.
$4$. With $M$ as the center and $MX$ (or $MY$) as the radius,draw a circle. This circle will intersect the circle with center $X$ at points $A$ and $B$,and the circle with center $Y$ at points $C$ and $D$.
$5$. Join $XA$ and $XB$ to get the tangents from $X$ to the circle centered at $Y$. (Note: Since the circles are separate,tangents from the center of one circle to the other are drawn by finding the intersection points of the auxiliary circle with the target circle).
$6$. Join $YC$ and $YD$ to get the tangents from $Y$ to the circle centered at $X$.
$1$. Draw a line segment $\overline{ XY } = 11\, cm$.
$2$. Draw a circle with center $X$ and radius $4\, cm$,and another circle with center $Y$ and radius $3\, cm$.
$3$. Find the midpoint $M$ of $\overline{ XY }$ by drawing the perpendicular bisector of $\overline{ XY }$.
$4$. With $M$ as the center and $MX$ (or $MY$) as the radius,draw a circle. This circle will intersect the circle with center $X$ at points $A$ and $B$,and the circle with center $Y$ at points $C$ and $D$.
$5$. Join $XA$ and $XB$ to get the tangents from $X$ to the circle centered at $Y$. (Note: Since the circles are separate,tangents from the center of one circle to the other are drawn by finding the intersection points of the auxiliary circle with the target circle).
$6$. Join $YC$ and $YD$ to get the tangents from $Y$ to the circle centered at $X$.
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