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Mathematics

Assertion (A) : A, B and C are three points on the circumference of a circle such that BC is diameter of the circle. If AC = 4 cm and AB = 3 cm, then diameter BC = 4 cm + 3 cm.

Reason (R) : Angle BAC = angle of semi-circle = 90° and so BC2 = AB2 + AC2

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Circles

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Answer

Given, AC = 4 cm and AB = 3 cm

Since BC is the diameter, angle BAC is a right angle.

Triangle ABC is a right triangle with hypotenuse BC.

Using Pythagoras theorem,

BC2 = AB2 + AC2

So, reason (R) is true.

⇒ BC2 = 32 + 42

⇒ BC2 = 9 + 16

⇒ BC2 = 25

⇒ BC = 25\sqrt{25}

⇒ BC = 5 cm.

So, assertion (A) is false.

∴ A is false, but R is true.

Hence, option 4 is the correct option.

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