? asked in Science & MathematicsPhysics · 1 decade ago

Find the area f the shaded shape ABP?

The Points A and B lie on the circumference of a circle centre C.

Tangents are drawn to the circle at A and B and intersect at the point P.

The radius of the circle is 8cm and the angle at the centre subtended by AB is 135 degrees.

Find the area of the shaded shape ABP.

If someone could please help me with this Question i would appreiciate it. Thank you.

Ian

Update:

Answer ends up to be 79.1 cm^2.

2 Answers

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  • NoELCE
    Lv 5
    1 decade ago
    Favorite Answer

    Length of the tangent , AP= 8 tan(135/2) = 19.3137

    1/2 Chord AB = AP cos (135/2)

    AB = 2 (19.3137) cos (135/2) = 14.782

    Altitude H = AP sin (135/2) = 17.8435

    Area ABP = 1/2 (AB)(H)

    substitute values:

    Area ABP = 1/2 x 14.782 x 17.8435 = 131.882 not anyway near your expected answer.

    THIS MEANS THE SHADED AREA IS NOT JUST (ABP) This means your shaded area is BOUNDED by ARC AB and the tangents AP and BP

    Therefore:

    The whole area = 1/2 AP (R) x 2 units = AP ( R)

    Area, Aw = 19.3137 (8) = 154.5096 sq cm

    Area of the Sector, As = pi R^2 (135/360)

    As = pi (8^2) (3/8) = 75.398 sq cm

    Net area = Aw - As

    Net area = 154.5096 - 75.398

    Net area = 79.1 sq cm *******ANSWER

    *******************************************

    Next time you provide the figure or at least describe it fully.

    OK? I hope I helped you on this.

    BYE BYE

  • 1 decade ago

    tan(135/2)=AP/8

    =>AP=8*tan67.5

    =8*2.4142

    =19.314cm

    APBC=2 * 1/2 * 19.314* 8

    = 154.51 cm^2

    ABC= 135/360 * pi * 8^2

    = 25.13cm^2

    APB= 154.51-25.13

    = 129.38cm^2

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