Assertion (A): Angle BOC = 90°.

Reason (R): OC² = 3² + 4² = 25

OB² = 6² + 8² = 100

OC² + OB² = 125 = BC²

1. A is true, but R is false.

2. A is false, but R is true.

3. Both A and R are true, and R is the correct reason for A.

4. Both A and R are true, and R is the incorrect reason for A.

Given, OD = 3 cm and DC = 4 cm

According to Pythagoras theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

⇒ Hypotenuse² = Base² + Height²

In Δ ODC,

⇒ OC² = OD² + DC²

⇒ OC² = 3² + 4²

⇒ OC² = 9 + 16

⇒ OC² = 25

⇒ OC = $\sqrt{25}$

⇒ OC = 5 cm

Similarly, it it given that OA = 6 cm and AB = 8 cm

In Δ OAB,

⇒ OB² = OA² + AB²

⇒ OB² = 6² + 8²

⇒ OB² = 36 + 64

⇒ OB² = 100

⇒ OB = $\sqrt{100}$

⇒ OB = 10 cm

Squaring all sides of triangle BOC,

⇒ OB² = 10² = 100

⇒ OC² = 5² = 25

⇒ BC² = $(5\sqrt{5})^2$ = 125

Since,

⇒ BC² = OC² + OB²

Since, sides of triangle BOC, satisfy pythagoras theorem. So, BOC is a right angle triangle with BC as hypotenuse.

∴ ∠BOC = 90°.

∴ Both A and R are true, and R is the correct reason for A.

Hence, option 3 is the correct option.