# geometry

posted by .

A point P is given outside of a circle Γ. A tangent from P to Γ touches Γ at T with PT=45. A line from P cuts Γ at the 2 points A,B. If PA=25, what is the length of PB?

• geometry -

81

• geometry -

PT^2 = PA * PB

PT = 45
PA = 25
PB = (45 * 45)/25
= 81 units

## Similar Questions

1. ### GEOMETRY......circle

Circles Γ1 and Γ2 intersect at 2 distinct points A and B. A line l through A intersects Γ1 and Γ2 at points C and D, respectively. Point E is the intersection of the tangent to Γ1 at C and the tangent to Γ2 …
2. ### Math

Let AB be the diameter of circle Γ1. In the interior of Γ1, there are circles Γ2 and Γ3 that are tangent to Γ1 at A and B, respectively. Γ2 and Γ3 are also externally tangent at C. This exterior tangent …
3. ### math

Let AB be the diameter of circle Γ1. In the interior of Γ1, there are circles Γ2 and Γ3 that are tangent to Γ1 at A and B, respectively. Γ2 and Γ3 are also externally tangent at the point C. This …
4. ### Math (Geometry)

A point P is given outside of a circle Γ. A tangent from P to Γ touches Γ at T with PT=45. A line from P cuts Γ at the 2 points A,B. If PA=25, what is the length of PB?
5. ### Math

P is a point outside of circle Γ. The tangent from P to Γ touches at A. A line from P intersects Γ at B and C such that m∠ACP = 120∘. If AC=16 and AP=19, find the radius of the circle.
6. ### heeeeeeeeeeeeelp math

P is a point outside of circle Γ. The tangent from P to Γ touches at A. A line from P intersects Γ at B and C such that ∠ACP=120∘. If AC=16 and AP=19, then the radius of Γ can be expressed as a√b/c …
7. ### heeeeeelp math

is a point outside of circle Γ. The tangent from P to Γ touches at A. A line from P intersects Γ at B and C such that ∠ACP=120 ∘. If AC=16 and AP=19, then the radius of Γ
8. ### heeeeeeelp math

P is a point outside of circle Γ. The tangent from P to Γ touches at A. A line from P intersects Γ at B and C such that ∠ACP=120 ∘. If AC=16 and AP=19, then the radius of Γ can be written as a root b/c …
9. ### math

Two congruent circles Γ1 and Γ2 each have radius 213, and the center of Γ1 lies on Γ2. Suppose Γ1 and Γ2 intersect at A and B. The line through A perpendicular to AB meets Γ1 and Γ2 again at …
10. ### Math

Γ 1 is a circle with center O 1 and radius R 1 , Γ 2 is a circle with center O 2 and radius R 2 , and R 2 <R 1 . Γ 2 has O 1 on its circumference. O 1 O 2 intersect Γ 2 again at A . Circles Γ 1 and Γ …

More Similar Questions