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please solve this geomentry sun?

1)triangle ABC with AB=AC=10 cm and has been inscribed in a circle. find the radius of the circle

2)PQ is the chord of length 8 cm of a circle of r=5 cm. the tangent at P and Q interdect at a point T . find the TP

3)the ratio of the number of sides of regular polygon is 1:2, abd the ratio of the sum of the interior angles is 3:8. find the numbr of sides

THANKS IN ADVANCE

1 Answer

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  • Anonymous
    7 years ago
    Favorite Answer

    1) See figure. Since no angle has been given, you can inscribe any isosceles triangle, including one whose sides have joined into a single line, which is the diameter. If one side is 10(the diameter), then half that is 5cm.

    2) See the figure. The chord is split in half by the line extending from the center to the intersection point, 4cm each.

    Radius is 5, which is the hypotenuse. Since PNO is a right triangle, ON can be calculated from Pythagorean theorem, which turns out 3.

    Now we compare the edges of two similar triangles: OPN and OTP since they share two edges and a common angle.

    PN/NO = TP/PO

    Plug in numbers

    4/3 = TP / 5

    Solving for TP gives us 20/3

    Attachment image
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