Question

Draw a circle as shown in figure 3.62. Draw a chord AB. Take any point on the circle. Draw inscribed angle abc, measure it and note the measure.​

Answer 1

Answer:

m(arc AB) = m(arc BC) = 120º

Now,

m(arc AB) + m(arc BC) + m(arc CA) = 360º  

⇒ 120º + 120º + m(arc CA) = 360º

⇒ 240º + m(arc CA) = 360º

⇒ m(arc CA) = 360º − 240º = 120º

∴ m(arc AB) = m(arc BC) = m(arc CA)

⇒ arc AB ≅ arc BC ≅ arc CA         (Two arcs are congruent if their measures are equal)

⇒ chord AB ≅ chord BC ≅ chord CA      (Chords corresponding to congruent arcs of a circle are congruent)

∴ ∆ABC is an equilateral triangle.          (All sides of equilateral triangle are equal)

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation: