Technical Drawing III 9 L i nk i ng c i r c umf e r e n c e s and s t r a i gh t l i n e s Link a circumference and a straight line with an arc whose radius is less than the radius of the circumference Given a circumference with radius m, the line AB and the arc radius r, follow these steps to link the circumference and the line: Step 1. Draw a parallel line to AB at a distance r. Step 2. Use centre point O and a radius equal to the sum of the radii m and r. Draw an arc that intersects the parallel line at point C. Step 3. Draw the segment OC that intersects the circumference at D. Step 4. Draw a perpendicular line to the parallel line that passes through point C. Label point E. Step 5. Use centre point C and radius r. Draw an arc that links the points D and E. Link a circumference and a straight line with an arc whose radius is greater than the radius of the circumference Given a circumference with centre F and radius p, the line AB and the arc radius q, follow these steps to link the circumference and the line: Step 1. Draw a line parallel to AB at a distance q. Step 2. Use centre point F and a radius equal to the difference between q and p. Draw an arc that intersects the parallel line at point G. Step 3. Draw the line FG that intersects the circumference at H. Step 4. Draw a perpendicular line to the parallel line that passes through point G. Label point J. Step 5. Use centre point G and radius q. Draw an arc that links the points H and J. Link two circumferences with an arc of a smaller radius Given two circumferences with centres N and M, and radii n and m, respectively, and the arc radius r, follow these steps to link the two circumferences: Step 1. Use centre point N and a radius equal to the sum of the radii n and r. Draw an arc. Step 2. Use centre point M and a radius equal to the sum of m and r. Draw an arc that intersects the previous arc at point A. Step 3. Draw the rays NA and MA. Where the lines intersect the circumferences, label the points B and C, respectively. Step 4. Use centre point A and radius r. Draw an arc that links the points B and C. Link two circumferences with an arc of a greater radius Given two circumferences with centres X and Y, and radii x and y, respectively; and the arc radius r, follow these steps: Step 1. Use centre point X and a radius equal to the difference between radii r and x. Draw an arc. Step 2. Use centre point Y and a radius equal to the difference between radii r and y. Draw an arc that intersects the previous arc at point Z. Step 3. Draw the lines XZ and YZ . Where the lines intersect the circumferences, label the points P and Q, respectively. Step 4. Use centre point Z and radius r. Draw an arc that links the points P and Q. r Z x X P y Y Q q G B J A H F p r m O D C B E A r m n C B M A N
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