Assertion: Points A(6, 4), B(-4, -6) and C(4, 6) are such that AB =$\sqrt{200}$, BC= $\sqrt{208}$, AC= $\sqrt{8}$, Since AB+BC>AC, points A, B and C from a triangle.

Reason: If $B{C}^2=A{B}^2+A{C}^2$, then $\Delta ABC$ is a right triangle, right angled at A.

Q.

Assertion: If AB = CD, then BE = DE and AE = CE, where E is the point of intersection of AD and BC.

Reason: Angles in the same segment are equal.


Which of the following options is correct?

Q. Assertion (A)
In an isosceles ∆ABC, if ∠C = 90°, then AB² = 3AC².
Reason (R)
In an isosceles ∆ABC, if AC = BC and AB² = 2AC², then ∠C = 90°.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A)
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion: If AD is a median of ∆ABC, then AB + AC > 2AD.
Reason: The angles opposite to equal sides of a triangle are equal.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Q. Assertion: $\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}but\overrightarrow{\tau }\ne \overrightarrow{F}\times \overrightarrow{r}.$
Reason: Cross product of a vector is commutative.

Q.

Assertion: Area of the triangle whose
vertices are $A(\frac{-3}{2},3),B(6,-2)$ and $C(-3,4)$ is 0
Reason : The points A, B and C are collinear