By the end of this guide, you will be able to confidently solve problems involving the lengths of secant segments, tangents, and their relationships both inside and outside the circle.
The fundamental rule for secant segments intersecting outside a circle is that the product of the entire secant length and its external portion is constant: 1. Apply the Segments of Secants Theorem When two secant segments ( ABcap A cap B CDcap C cap D ) are drawn from a common exterior point ( ), their parts follow a specific proportionality. 10-5 additional practice secant lines and segments
[ \textSecant 1: whole = 15, \text external = 9 \ \textSecant 2: whole = 12, \text external = x ] By the end of this guide, you will
From point P outside circle O, secant PAB has PA = 15, PB = 5. Another secant PCD has PC = 12. Find PD (the external segment). [ \textSecant 1: whole = 15, \text external
If from point P outside the circle, tangent PT touches at T, and secant PAB goes through A (far) and B (near): [ (PT)^2 = PA \times PB ]
Try these problems on your own. They mimic the style of a "10-5 additional practice" worksheet.
Let’s apply these theorems to typical "additional practice" problems.
By the end of this guide, you will be able to confidently solve problems involving the lengths of secant segments, tangents, and their relationships both inside and outside the circle.
The fundamental rule for secant segments intersecting outside a circle is that the product of the entire secant length and its external portion is constant: 1. Apply the Segments of Secants Theorem When two secant segments ( ABcap A cap B CDcap C cap D ) are drawn from a common exterior point ( ), their parts follow a specific proportionality.
[ \textSecant 1: whole = 15, \text external = 9 \ \textSecant 2: whole = 12, \text external = x ]
From point P outside circle O, secant PAB has PA = 15, PB = 5. Another secant PCD has PC = 12. Find PD (the external segment).
If from point P outside the circle, tangent PT touches at T, and secant PAB goes through A (far) and B (near): [ (PT)^2 = PA \times PB ]
Try these problems on your own. They mimic the style of a "10-5 additional practice" worksheet.
Let’s apply these theorems to typical "additional practice" problems.