Find the area of a circle whose area equals the half of the sum of the areas of two circles with radii 2 and 3.

The area of a circle is 20.41 units.

Step-by-step explanation:

Formula

Where r is the radius of a circle.

As given

First take when the radius of a circle is 2 unit.

radius = 2 units

Put in the formula

                                    = 12.56 unit

Second take when the radius of a circle is 3 unit.

radius = 3 units

Put in the formula

                                    = 28.26 unit

As given

The area of a circle whose area equals the half of the sum of the areas of two circles with radii 2 and 3.

Put the value in the  above

Area of a circle = 20.41 units

Therefore the area of a circle is 20.41 units.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.