Question

In the diagram below, an and bc are tangent to o. What is the measure of adc

Answer 1

Look at the attached graphic.

40° = ½ (ADC -140°)
40° = ½ ADC -70°
110° = ½ ADC
ADC = 220°

Answer 2

mADC = 220°

Explanation:

In the given diagram AB and BC are tangents to the given circle O. We have to find the measure of arc ADC.

By theorem of tangents and arcs.

m∠ABC =
`(1)/(2)` [m ADC- m AC ]

Since it is given in the question

∠ABC = 40 & AC = 140°

Therefore, 40 =
`(1)/(2)` [ m ADC - 140 ]

40 × 2 = m ADC - 140

80 + 140 = m ADC

mADC = 220°