In rectangle ABCD AB = 4 and BC = 5. Point P is the interior point of segment BC. A circle is inscribed

In rectangle ABCD AB = 4 and BC = 5. Point P is the interior point of segment BC. A circle is inscribed in the quadrangle APCD. Calculate the distance from the center of the circle to point A

From the center of the circle, point O, draw perpendiculars OP, OM and OH to the sides of the rectangle.

The radius of the inscribed circle is equal to half of the side AB of the rectangle. OR = OM = OH = AB / 2 = 2 cm.

Quadrangle ORSM square, then РС = ОМ = 2 cm, which means BP = ВС – РС = 5 – 2 = 3 cm.

The length of the segment AH = BP = 3 cm.

In the right-angled triangle AON, we determine the length of the hypotenuse OA.

OA ^ 2 = AH ^ 2 + OH ^ 2 = 9 + 4 = 13.

ОА = √13 cm.

Answer: The distance from the center of the circle to point A is √13 cm.