Circles Review of Angles and Tangents

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

In the figure,PA and PB are the tangents to a circle of center 'O'. ∠AOB= 120⁰ then ∠APB =

• 60⁰

• 30⁰

• 120⁰

• 75⁰

• A
• B
• C
• D

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

In the diagram, PQ and QR are tangents to a circle at P and R respectively. Which of the following statements is correct?

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

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 PQR is a tangent to the circle. Find the value of x and y.

• x = 65o, y = 115o

• x = 50o, y = 40o

• x = 20o, y = 50o

• x = 40o, y = 50o

• x = 50o, y = 80o

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