Question

Assertion (A)	Reason (R)
In the given figure, a quad. ABCD is drawn to circumscribe a given circle, as shown. Then, AB + BC = AD + DC.	In two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (А).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is false and Reason (R) is true.

Explanation:

Assertion (A) is false. For a quadrilateral with an incircle (a tangential quadrilateral) the correct relation is AB + CD = BC + DA, this follows because tangents from each vertex to the circle are equal (if the incircle touches AB, BC, CD, DA at P, Q, R, S then AP = AS, BP = BQ, CQ = CR, DR = DS, which on adding gives AB + CD = AD + BC).

Reason (R) is true: if a chord of a larger concentric circle is tangent to the smaller circle at P, then OP (common centre O) is perpendicular to the chord and so P is the midpoint of the chord, i.e. the chord is bisected at the point of contact.

Because (A) is false and (R) is true.