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Segments in a Circles

This lab is to investigate the length of segments formed by two secants and a secant and a tangent.

• Construct circle A.
• Construct points C, D, E, and F on the circle and place them in consecutive order.
• Construct secants CD and EF have them intersect outside the circle at point G so that C is between G and D, and F is between G and E.
• Construct segments DF and CE to form triangles CEF and CDG

Are these triangles similar? Why? Will they always be similar? Why or why not?

Write the proportions of the corresponding sides.

Find the cross product of the segments that are part of the secants (do not use the proportions with DF and CE).

Use calculate to confirm this product in your sketch.

Explain this product in your own words.

• Construct circle A.
• Construct raduis AC
• Construct a tangent at point C.
• Construct secant DE to intersect the tangent at point F
• Move point E so that E is between F and D.
• Hide the radius.
• Construct chords CE and CD to create the triangles FDC and FCE.

Are these triangles similar? Why? Will they always be similar? Why or why not?

Write the proportions of the corresponding sides.

Find the cross product of the segments that are part of the secant and the tangent (do not use the proportions with CE and CD).

Use calculate to confirm this product.

Explain this product in your own words.