Circle Angles Tangent Decant

The lines PA and PB are tangents to the circle with centre O at A and B. If ∡OAB = 32°, find ∡APB.

• 32°

• 58°

• 64°

• 90°

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

Diagram shows a circle with centre O and ABC is a tangent to the circle at B. Given that BD=DE, find the value of X.

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

Assume that lines that appear to be tangent are tangent. O is the circle. What is the value of x?

• 90

• 140

• 220

• 360

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

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

• 60⁰

• 30⁰

• 120⁰

• 75⁰

• 50

• 115

• 65

• 130

In the figure,PA and PB are the tangents to a circle of centre 'O'. If ∠APB = 48⁰ then ∠AOP =

• 68⁰

• 66⁰

• 56⁰

• 76⁰