PQRS is an isosceles trapezium with sides PQ and RS parallel and side PS = side QR. a circle is drawn in picside the trapezium that touches the sides of the trapizium from inside. if PQ is 8 and RS is 18, what is the radius of the circle?
Answers
Given : PQRS is an isosceles trapezium with sides PQ and RS parallel and side PS = side QR. a circle is drawn in picside the trapezium that touches the sides of the trapizium from inside .PQ is 8 and RS is 18,
To find : radius of the circle
Solution:
As all sides are tangent to circle
Hence Sum of opposite sides is Equal
=> QR + PS = PQ + RS
QR = PS isosceles trapezium
=> 2QR = 8 + 18
=> QR = 13
if we Draw perpendicular from P & Q on RS as X & Y
then XY = PQ = 8
SX = RY & SX + RY = RS - XY = 18 - 8 = 10
=> SX = RY = 5
PS = 13
PX² = PS² - SX²
=> PX² = 13² - 5²
=> PX² = 12²
=> PX = 12
12 will be diameter of Circle
Radius of Circle = 12/2 = 6 cm
radius of the circle = 6 cm
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