Question

Given that AB = 12 cm, BN = 8 cm, M is the mid-point of 12 S S OB, find AM (A) 6.5 cm (B) 7.5 cm (C) 10 cm (D) 9.5 cm 6.5 B M O M No 3 5 8 cm​

Answer 1

Answer:

Step-by-step explanation:

=24 cm

Answer 2

Answer:

Option (A) 6.5

Step-by-step explanation:

Given AB = 12cm and BN = 8cm

Let radius of circle be r cm

So CN = 2r cm

Now using Tangent Secant Theorem,

AB² = BN • ( BN + CN )

12² = 8 • ( 8 + 2r )

144/8 = 2( 4 + r )

18/2 = 4 + r

9 - 4 = r

r = 5cm

So , OB = 13 cm

Drop a perpendicular on AB from point M

Now ∆ABO ~ ∆ QBM

AAA Criterion

So,

BO/BM = AO/QM

Given M is the midpoint of OB

So,

OM = MB = 13/2 cm

Now,

BO/BM = AO/AM

13/13/2 = 5/AM

AM = 5/2 cm

Join A and M

In ∆ AQM

AQ ² + QM ² = AM ²

6² + (5/2)² = AM²

169/4 = AM²

13/2 = AM

AM = 6.5 cm