Question

Find the possible length pairs of AC and CB, for the following diagram. Here, O is the radius of the circle.

• A. 3 units and 4 units , respectively.
• B. Both as 5 units.
• C. 4 units and 3 units , respectively.
• D. Both as 7 units.

Answer 1

Answer: (B), (D)

Both as 7 units.

The angle subtended by the diameter AB to C on the circle is equal to ${90}^o.$

Hence, $\angle C={90}^o.$

Given: $\angle B={45}^o$
$\therefore$ For $△ACB,$
$\angle A={180}^o-{90}^o-{45}^o={45}^o$

As the two angles are equal in measure, the opposite sides AC and CB are equal in length.

Hence, both option (b) and (c) are possible.