Question

In the below figure OB = 13 cm; OP = 12 cm and OP⊥AB, then the value of AB is

• A. 5 cm
• B. 100 cm
• C. 10 cm
• D. 75 cm

Answer 1

The Correct Option is C

To solve the problem, we need to find the length of chord $AB$ in the circle given:

1. Information Given:

$OB = 13$ cm (radius),

$OP = 12$ cm (perpendicular from the center to the chord),

$OP \perp AB$ (so $P$ is the midpoint of $AB$)

2. Applying Pythagoras Theorem:

In right triangle $\triangle OBP$, we apply the Pythagorean theorem:

$ OB^2 = OP^2 + PB^2 $

$ 13^2 = 12^2 + PB^2 $

$ 169 = 144 + PB^2 $

$ PB^2 = 169 - 144 = 25 $

$ PB = \sqrt{25} = 5 $ cm

3. Finding Full Length of AB:

Since $P$ is the midpoint of $AB$ (because $OP$ is perpendicular from the center),

$ AB = 2 \times PB = 2 \times 5 = 10 $ cm

Final Answer:
The length of $AB$ is $ {10 \, \text{cm}} $