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Which of the following statements is/are true? A: The incircle of a triangle touches each side of the triangle at mid-point. B: ABCD is quadrilateral. If A, B and C are on the circumference of a circle, D is the center of the circle and AB and BC are smaller than radius of circle, then ∠ABC will be (180 – smaller ∠ADC/2). C: Angle made by a tangent on any chord of a circle will never be right angle.

Which of the following statements is/are true? A: The incircle of a triangle touches each side of the triangle at mid-point. B: ABCD is quadrilateral. If A, B and C are on the circumference of a circle, D is the center of the circle and AB and BC are smaller than radius of circle, then ∠ABC will be (180 – smaller ∠ADC/2). C: Angle made by a tangent on any chord of a circle will never be right angle. Correct Answer Only B

CONCEPT:

Properties of circle, chord, tangents, inradius, and circumradius.

CALCULATION:

A: The incircle of a triangle touches each side of the triangle at that point, where the altitude from the center of incircle is formed at each side.

B:

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Larger ∠ADC is equal to (360° – smaller ∠ADC) and ∠ABC is equal to larger ∠ADC/2. So, ∠ ABC will be equal to (360° – smaller ∠ADC)/2. So, ∠ABC = (180° – smaller ∠ADC/2).

C: The largest chord of a circle is its diameter and the angle made by a tangent on diameter of a circle is always right angle.

Hence, only statement B is true.

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