In the figure below, if C is the center of the circle and 30 < C < 60, then which of the following expresses all possible values of a? Select one: A. 50 < a < 70 B. …

Question

asked Aug 18, 2021 215k views

1 Answer

PAC · Answer 1 · 2021-08-24T02:38:38+0000

Answer:

Option C.

Explanation:

In the given figure C is the center of the circle.

Let A and B are two points on the circle, such that

$\angle A=a^(\circ),\angle B=b^(\circ)$

Since CA and CB are radius of the circle, therefore ABC is an isosceles triangle.

$\angle A=\angle B=a^(\circ)$

Using angle sum property,

$\angle A+\angle B+\angle C=180^(\circ)$

$a^(\circ)+a^(\circ)+\angle C=180^(\circ)$

$2a^(\circ)=180^(\circ)-\angle C$

Divide both sides by 2.

$a^(\circ)=(180^(\circ)-\angle C)/(2)$

It is given that

30<C<60

$\Rightarrow 180-30>180-C>180-60$ (Subtract from 180)

$\Rightarrow 150>180-C>120$

$\Rightarrow (150)/(2)>(180-C)/(2)>(120)/(2)$ (Divide by 2)

$\Rightarrow 75>a>60$

$\Rightarrow 60<a<75$

Hence, the correct option is C.