Question

What is the measure of minor arc BD?
Angle BCD is a circumscribed angle of circle A. Angle BCA
measures 40°
B
40°
© 50°
80°
100°

Answer 1

Answer:

$minor\ arc\ BD=100^o$

Step-by-step explanation:

The picture of the question in the attached figure

we know that

A circumscribed angle is the angle made by two intersecting tangent lines to a circle

so

In this problem

BC and CD are tangents to the circle

BC=CD ----> by the Two Tangent Theorem

That means

Triangle ABC and Triangle ADC are congruent

so

$m\angle BAC=m\angle DAC$

Find the measure of angle BAC

In the right triangle ABC

$m\angle BAC+m\angle BCA=90^o$

substitute given value

$m\angle BAC+40^o=90^o$

$m\angle BAC=90^o-40^o=50^o$

Find the measure of angle BAD

$m\angle BAD=2m\angle BAC$

$m\angle BAD=2(50^o)=100^o$

Find the measure of minor arc BD

we know that

$minor\ arc\ BD=m\angle BAD$ -----> by central angle

therefore

$minor\ arc\ BD=100^o$

Answer 2

Answer:

the answer is 100, D of e2020

Step-by-step explanation: