Question

In the given figure, PAQ is the tangent. BC is the diameter of the circle. if BAQ = 60°, find ABC

(A) 25° (B) 30°

(C) 45° (D) 60°​

Answer 1

Step-by-step explanation:

Given- BC is the diameter of a circle with centre O.

∠ABC&∠ADC are the angles, subtended by arc AC to the circumference of the same segment of the circle. ∠BAO=60 °

.

To find out- ∠ADC=?

Solution- In ΔBAO we have OA=OB (radii of the same circle).

∴∠ABO=∠AOB. i.e 4 ∠ABO+∠AOB=2∠ABO.

So 2∠ABO+∠BAO=180 °

(angle sum property of triangles). ⟹2∠ABO+60°

=180 °

⟹∠ABO=60 °

Again ∠ABO=∠ADC, since the angles, subtended by an arc to the circumference of the same segment of the circle, are equal

∴∠ADC=60 °

.

Ans- Option C°