A circle is inscribed in trapezoid PQRS. If PS = QR = 25 cm, PQ = 18 c

1.	A circle is inscribed in trapezoid PQRS. If PS = QR = 25 cm, PQ = 18 cm andSR = 32 cm, the length of the diameter of the circle?
Answer» Given: PS = QR = 25 cm, PQ = 18 cm and SR = 32 cm. Drawing perpendiculars from P and Q to meet SR at X and Y respectively. Let AB be the diameter of the circle, where AB = PX. We see that XY = PQ = 18. Also SX = YR which gives us SX = YR = (32 – 18)/ 2 = 7 cm By applying the Pythagorean Theorem in ∆ PXS, we get PX2+ 72= 252 PX2= 576 PX = 24. As PX = AB and AB is the diameter of the circle, therefore the diameter of the circle is 24 cm.

A circle is inscribed in trapezoid PQRS. If PS = QR = 25 cm, PQ = 18 cm andSR = 32 cm, the length of the diameter of the circle?

Answer»

Given: PS = QR = 25 cm, PQ = 18 cm and SR = 32 cm.

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

Let AB be the diameter of the circle, where AB = PX.

We see that XY = PQ = 18.

Also SX = YR which gives us SX = YR = (32 – 18)/ 2 = 7 cm

By applying the Pythagorean Theorem in ∆ PXS, we get

PX2+ 72= 252

PX2= 576

PX = 24.

As PX = AB and AB is the diameter of the circle, therefore the diameter of the circle is 24 cm.