Question

A circle is inscribe in trapezoid PQRS. If
PS = QR = 25 cm,
PQ = 18 cm and
SR = 32 cm, what is the length of the diameter of
the circle?
o
S
(a) 14 cm
( 24 cm
R
(b) 5 cm
(d) 1674 cm​

Answer 1

Answer:

hope it helps you

Step-by-step explanation:

Given:PQRS is a Trapezoid.

PQ=QR=25cm

SR=32cm

PQ=18cm

Draw perpendiculars from P and Q to meet SR at X and Y respectively.

AB is diameter of circle

PX=AB

Also ,PQ=XY

XY=18.....(1)

Also SX = YR

SX = YR =half of (SR-XY)=7cm

SX=7cm...(2)

InRightangle△PXS

PS

2

=SX

2

+PX

2

25

2

=7

2

+PX

2

[From(2)]

⇒PX

2

=625−49

⇒PX

2

=576

⇒PX=24

Since PX=AB

AB=24cm id diameter of cicle.

Hence option (C) is the correct answer