The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer. Assertion (A) Reason (R) In the given figure, ∆ABC is given with AB=AC and BA is produced to D, such that AB=AD. Then, ∠ BCD=90°. In the given figure AB=AC and D is a point on BC produced. Then, ABAD.

Question

The question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer. Assertion (A) Reason (R) In the given figure, ∆ABC is given with AB=AC and BA is produced to D, such that AB=AD. Then, ∠ BCD=90°. In the given figure AB=AC and D is a point on BC produced. Then, AB>AD.

Philoid · Accepted Answer

According to the question,

AB = AC

∠ACB = ∠ABC (i)

Now, ∠ACD >∠ACB =∠ABC (Side BC is produced to D)

And, In ∆ADC, side DC is produced to B

∠ACB>∠ADC (ii)

∠ABC>∠ADC

Now, using (i) and (ii),

AD >AB

Hence, the reason is wrong but the assertion is true.

∴ Option C is correct