Question

A circle is centered on point b . Points a,c, and d lie on its circumference . If adc measure 61 then what does abc measure.

Answer 1

`\angle ABC = 122^\circ`

Explanation:

Given

`\angle ADC = 61^\circ`

See attachment for circle

Required

Find
`\angle ABC`

From the attachment, we can see that:

`\angle ADC` is at the circumference

`\angle ABC\\` is in at the center

From cyclic theorems,

The relationship between ABC and ADC is:

`\angle ADC = (1)/(2) * \angle ABC`

Make ABC the subject

`\angle ABC = 2 * \angle ADC`

Substitute:
`\angle ADC = 61^\circ`

`\angle ABC = 2 * 61^\circ`

`\angle ABC = 122^\circ`