Math

posted by .

G is a circle with chord AB. P is a point outside of G such that PA is tangent to G and ?BPA=90°. If AB=48 and PB=8, what is the radius of G?

  • Math -

    The angle between a tangent and the chord at their point of contact is equal to half the angle at the centre.
    So once we find angle BAP it should not be that bad

    In right-angled triangle ABP , P = 90°
    let angle BAP = Ø
    sinØ = 8/48 = 1/6
    Ø = 80.4°
    so 2Ø or central angle = 160.8

    In triangle AOB , where O is the centre, and OA = OB = radius
    angle OBA = 9.59°

    by the sine law:
    OB/sin9.59° = 48/sin160.8°
    OB = 24.3

    The radius is 24.3 units

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. geometry

    In a circle with centre P,a chord AB is parallel to a tangent & inersects the radius drawn from a point of contact at the midpoint of the radius .If AB=12,FIND THE RADIUS OF THE CIRCLE.
  2. Radius

    Γ is a circle with chord AB. P is a point outside of Γ such that PA is tangent to Γ and ∠BPA=90∘. If AB=48 and PB=8, what is the radius of Γ?
  3. Maths

    G is a circle with chord AB. P is a point outside of G such that PA is tangent to G and ?
  4. 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.
  5. GEOMETRY CIRCLES PLEASE

    1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle 2. Circles a and b are tangent at point c. p is on circle a and q is on circle b such …
  6. GEOMETRY CIRCLE

    1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle 2. Circles a and b are tangent at point c. p is on circle a and q is on circle b such …
  7. GEOMETRY CIRCLES PLEASE

    HELP ME PLEASE. 1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle 2. Circles a and b are tangent at point c. p is on circle a and q is …
  8. Geometry about the circles

    1. Ab is a chord of a circle with center o and radius 52 cm . point m divides the chord ab such that am = 63 cm and mb=33 cm find om 2. A circle is inscribed in a triangle whose sides are 10, 10 and 12 units . a second smaller circle …
  9. Geometry about the circles

    1. Ab is a chord of a circle with center o and radius 52 cm . point m divides the chord ab such that am = 63 cm and mb=33 cm find om 2. A circle is inscribed in a triangle whose sides are 10, 10 and 12 units . a second smaller circle …
  10. GEOMETRY CIRCLES

    1. Ab is a chord of a circle with center o and radius 52 cm . point m divides the chord ab such that am = 63 cm and mb=33 cm find om 2. A circle is inscribed in a triangle whose sides are 10, 10 and 12 units . a second smaller circle …

More Similar Questions