Question

Draw a sufficiently large circle of any radius as shown in the figure below. Draw a chord AB and central ∠ACB. Take any point D on the major arc and point E on the minor arc.

i. Measure ∠ADB and ∠ACB and compare the measures. 

ii. Measure ∠ADB and ∠AEB. Add the measures. 

iii. Take points F, G, H on the arc ADB. Measure ∠AFB, ∠AGB, ∠AHB. Compare these measures with each other as well as with measure of ∠ADB. 

iv. Take any point I on the arc AEB. Measure ∠AIB and compare it with ∠AEB.

Answer 1

i. ∠ACB = 2 ∠ADB. 

ii. ∠ADB + ∠AEB = 180°. 

iii. ∠AHB = ∠ADB = ∠AFB = ∠AGB 

iv. ∠AEB = ∠AIB