Question

point o is the center of this circle. what is ( mangle bca )?
a. ( 56^circ )
b. ( 62^circ )
c. ( 72^circ )
d. ( 76^circ )

Explanation:

Step1: Find $\angle OBD$ and $\angle OAD$

Tangents are perpendicular to radii, so $\angle OBD = 90^\circ$, $\angle OAD = 90^\circ$.

Step2: Calculate $\angle AOB$

Sum of quadrilateral angles is $360^\circ$.
$$\angle AOB = 360^\circ - 90^\circ - 90^\circ - 56^\circ = 124^\circ$$

Step3: Relate $\angle BCA$ to $\angle AOB$

Inscribed angle is half central angle.
$$m\angle BCA = \frac{1}{2} \angle AOB$$

Step4: Compute final angle

$$m\angle BCA = \frac{1}{2} \times 124^\circ = 62^\circ$$

Answer:

B. $62^\circ$