Question

in the diagram below, AB and BC are tangent to O. Which equation could be solved to find y, the measure of ADC

Answer 1

A

Explanation:

∠ABC is formed by 2 tangents to the circle and is measured as

∠ABC =
`(1)/(2)` (m arc ADC - m arc AC ), that is

`(1)/(2)` (y - 119) = 61 → A

Answer 2

A.
`(1)/(2)(y^(\circ)-119^(\circ))=61^(\circ)`

Explanation:

We have been given a diagram. We are asked to choose the equation that can be used to solve for y.

We know that measure formed by two intersecting tangents outside a circle is half the difference of corresponding arcs.

`m\angle ABC=(1)/(2)(\widehat{ADC}-\widehat{AC})`

`61^(\circ)=(1)/(2)(y^(\circ)-119^(\circ))`

Switch sides:

`(1)/(2)(y^(\circ)-119^(\circ))=61^(\circ)`

Therefore, option A is the correct choice.