Post a New Question

geometry

posted by .

Let O be the center of the circle Γ, and P be a point outside of circle Γ. PA is tangential to Γ at A, and PO intersects Γ at D. If PD=14 and PA=42, what is the radius of Γ.

  • geometry -

    In this case the secant - tangent theorem says

    PA^2 = PD x PC , where D in on the extension of PO as it hits the circle , making CD a diameter
    Let the diameter be 2x , (radius = x)
    (14)(2x+14) = 42^2
    28x + 196 = 1764
    28x = 1568
    x = 56

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. circle geometry

    Circles Γ1 and Γ2 intersect at 2 distinct points A and B. A line l through A intersects Γ1 and Γ2 at C and D, respectively. Let M be the midpoint of CD. The line MB intersects Γ1 and Γ2 again at E and …
  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. 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. maths

    Equilateral triangle ABC has a circumcircle Γ with center O and circumradius 10. Another circle Γ1 is drawn inside Γ such that it is tangential to radii OC and OB and circle Γ. The radius of Γ1 can be expressed …
  6. math

    Equilateral triangle ABC has a circumcircle Γ with center O and circumradius 10. Another circle Γ1 is drawn inside Γ such that it is tangential to radii OC and OB and circle Γ. The radius of Γ1 can be expressed …
  7. Maths

    Given circle Γ and a point P outside of Γ, 2 lines l1 and l2 are drawn such that both pass through P. l1 intersects Γ at A and B, and l2 intersects Γ at C and D, with C between D and P. If PA=44,PB=294 and PC=56, …
  8. 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
  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

Post a New Question