Circle Review!

Match the following

• Secant

• Tangent

• Chord

• Radius

Find the value of x.

Answer explanation

The measure of the inscribed angle is half the measure of the intercepted arc (arc it cuts off)

What is the m∠U?

• 38⁰

• 19⁰

• 76⁰

• 90⁰

Answer explanation

The measure of the inscribed angle is half the measure of the intercepted arc (arc it cuts off). So, the arc is 76 degrees and the central angle is also 76 degrees.

Find a and b.

• a=74⁰
  b=93⁰

• a=93⁰
  b=74⁰

• a=87⁰
  b=106⁰

• a=106⁰
  b=87⁰

Answer explanation

Opposite angles add up to 180 degrees in an inscribed qudrilateral.

Find m∠PRQ.

• 39°

• 90°

• 51°

• 15°

Answer explanation

Angle Q is 90 degrees so angle R = 180 - (90 + 39)

What is m∠RST?

• 86°

• 43°

• 172°

• 90°

Answer explanation

Angle RST and ROT intercept the same arc so they have the same measure.

Find the value of d.

Answer explanation

Angles J and M intercept the same arc and are congruent. Thus, 14d = 70.

Find m∠RPQ.

• 55°

• 70°

• 110°

• 145°

Answer explanation

The measure of arc RPQ is 70 degrees, so the measure of the larger arc is 360 - 70 = 290 degrees. The measure of angle RPQ is hal of 290 degrees.

Line segments AB and CB are tangent to the circle. If the radius of the circle is 15 in and DB = 39 in, what is the value of AB?

• 32

• 36

• 42

• 25

Answer explanation

The tangent and radius meet at a right angle so use the Pythagorean theorem to find the missing side!

Polygon MNQP is a square. If the radius of the circle is 5 cm, what is the length of QR?

• 10 cm

• 2.5 cm

Answer explanation

RP = 5 because it is a radius. It is also half of the side of the square, so PQ = 10. Use the Pythagorean theorem to find the hypotenuse.