Question

ABD is formed by a tangent and a secant intersecting outside of a circle. If minor arc AC = 72° and minor arc CD = 132°, what is the measure of ∠ABD? A) 30° B) 36° C) 42° D) 48°

Answer 1

Answer:

42

Step-by-step explanation:

......

Answer 2

Answer:

(B) 36°

Step-by-step explanation:

AB is a secant to the circle and B D is the tangent.

Consider O as the center of the circle.

then ∠A O C =72° and ∠ COD =132°

As OD ⊥ B D [ Line from the center to the point of contact of tangent are perpendicular.]

∠ OD B= 90°

In Δ A O C

O A = O C [radii of same circle]

∠ O A C = ∠ O C A [ If sides are equal angle opposite to them are equal]

∠ O A C  + ∠ O C A +∠ A O C =180° [ sum of angles of triangle is 180°]

2∠O AC+72° = 180°

∠O AC = 108°÷2

∠O AC = 54°

In Δ A B D

∠A B D + ∠A DB+ ∠BAD =180° [angle sum property of triangle]

∠A B D +90° +54° =180°

∠A B D = 180 - 144°

∠A B D =36°

Option (B) is correct.