Angles and Tangents to a Circle

If a line is tangent to a circle, then it is ________ to the radius drawn to the point of tangency.

• parallel

• adjacent

• supplementary

• perpendicular

Using lines tangent to the circle, find the value of x.

• 57

• 137

• 47

• 257

Find a and b.

• a=74 degrees
  b=93 degrees

• a=93 degrees
  b=74 degrees

• a=87 degrees
  b=106 degrees

• a=106 degrees
  b=87 degrees

• A
• B
• C
• D

The diagram shows a circle with a straight line JKL is a tangent to a circle at K. Given \angle LKM=72\degree and \angle KMN=60\degree . Find the value of x and y.

The diagram shows two circles centred at A and B with radius 4cm and 8cm respectively. PQRS and TUV are common tangents to both circles and ∠PAQ=70°.

Calculate the value of y

The diagram shows PQ and RS are two tangents to a circle centred at O. Find the value of x, y and z.

• x = 66o, y = 24o, z = 8 cm

• x = 24o, y = 66o, z = 8 cm

• x = 66o, y = 24o, z = 16 cm

• x = 24o, y = 66o, z = 16 cm

Lines that appear to be tangent are​ tangent.

        What is the value of​ x?

Mathematical Equivalence

ON

Answer explanation

radii drawn to the point of tangency for right angles.

x = 360 - 90 - 90 - 120

x = 60

Line HK is tangent to circle C at point J.

Find each measure.

m∠KJM = ​ ​ (a)   _ , m∠MJN = ​ (b)   , m∠HJN = ​ (c)  

• 48

• 63

• 222

• 192

• 69

• 138