Question

Plz answer this question fast plzzz urgent

Answer 1

Answer:

AC = 12 cm

Step-by-step explanation:

Given:- A Circle with centre O, AB is a chord and BOC is the diameter and OD ⊥ AB such that, OD = 6 cm

Now,

Let the radius of this circle be r

then, it diameter = 2r

Now,

In ΔBOD and ΔBCA

∠ABC = ∠DBO

∠ODB = ∠CAB = 90° [BOC is the diameter, thus angle formed in a semicircle will be 90°]

Thus,

ΔBOD ~ ΔBCA [By A.A Similarity]

Thus,

BO/BC = DO/AC [Corresponding parts of similar Triangles]

Now, we know that,

BO = r

BC = 2r

DO = 6 cm

Thus,

r/2r = 6/AC

1/2 = 6/AC

Cross multiplying we get,

AC × 1 = 6 × 2

AC = 12 cm

Thus,

AC = 12 cm

Hope it helped and believing you understood it........All the best