geometry

posted by .

quadrilateral ABCD has right angles at B and D. If ABCD is kite-shaped with AB=AD=20 and BC=CD=15, find the radius of the circle inscribed in ABCD.

  • geometry -

    Join BD
    BD will be a line of symmetry and the centre of the inscribed circle will have to be on AC and have to be the midpoint of BD. Let that point be P
    BD^2 = 20^2 + 20^2 - 2(20)(20)cosA
    = 800 - 800cosA
    also BD^2 = 15^2+15^2-2(15)(15)cosC
    = 450-450cosC
    so 450-450cosC= 800-800cosA
    800cosA -450cosC = 350
    but C = 180-A
    cosC = cos(180-A) = -cosA
    800cosA +450cosA = 350
    CosA = .28 (nice)
    A = 73.7398°
    BD^2 = 800-800cosA = 800-800(.28) = 576
    BD = √576 = 24
    BP = 12


    Let r be the radius of the circle from P to line AB
    angle ABD = 53.13..°
    and BP, the hypotenuse of that little triangle is
    sin 53.13...° = r/12
    r = 12sin53.13..° = 12(.8) = 9.6

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Geometry

    The coordinates of the vertices of quadrilateral ABCD are A (-8, 8), B (-4, 8), C (-4, 4), D (-8, 4). The coordinates of the vertices of quadrilateral PQRS are P (-10, 10), Q (-2, 10), R (-2, 2), S (-10, 2). Which statement is correct?
  2. Geometry

    Circle O is inscribed is square ABCD, and at the same time, is circumscribed about square PQRS. WHich are is the smaller area, the region inside the inscribed circle minus the area of square PQRS or the are inside square ABCD minus …
  3. GEOmetry!!.....

    ABCD is a trapezoid with AB<CD and AB parallel to CD. Γ is a circle inscribed in ABCD, such that Γ is tangent to all four sides. If AD=BC=25 and the area of ABCD is 600, what is the radius of Γ?
  4. Geometry

    ABCD is a trapezoid with AB < CD and AB parallel to CD. \Gamma is a circle inscribed in ABCD, such that \Gamma is tangent to all four sides. If AD = BC = 25 and the area of ABCD is 600, what is the radius of \Gamma?
  5. Geometry

    In quadrilateral ABCD, we have AB = BC = CD = DA, AC = 14, and BD = 48. Find the perimeter of ABCD.
  6. geometry

    A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?
  7. geometry

    If rectangle ABCD has vertices A(6, 2), B(2, 2), and C(0, 6), explain how to find the coordinate for the fourth vertex. Then describe how to verify that the angles of ABCD are right angles.
  8. QUADRILATERAL MATHS

    ABCD is a quadrilateral with angle ABC a right angle. The point D lies on the perpendicular bisector of AB. The coordinates of A and B are (7, 2) and (2, 5) respectively. The equation of line AD is y = 4x − 26. find the area of quadrilateral …
  9. Geometry

    ABCD is a quadrilateral inscribed in a circle, as shown below: Circle O is shown with a quadrilateral ABCD inscribed inside it. Angle A is labeled x plus 16. Angle B is labeled x degrees. Angle C is labeled 6x minus 4. Angle D is labeled …
  10. Geometry

    Quadrilateral ABCD is a parallelogram. If adjacent angles are congruent, which statement must be true?

More Similar Questions