Question

A circle is circumscribed about an equilateral triangle $ABC$ and a point $P$ on the minor are joining $A$ and $B$, is chosen. Let $x=PA,y=PB$ and $z=PC$.($z$ is larger than both $x$ and $y$.)
Statement-$1$: Each of the possibilities $(x+y)$ grater than $z$, or less than $z$, is possible for some $P$.
Because
Statement-$2$: In a triangle ABC , sum of the two sides of a triangle is grater than the third and the third side is grater than the difference of the two.

• A. Statement-$1$- is true, Statement-$2$- is true and Statement-$2$- is correct explanation for Statement-$1$.
• B. Statement-$1$- is true, Statement-$2$ is true and Statement-$2$ is $NOT$ the correct explanation for Statement-$1$.
• C. Statement-$1$ is true ,Statement-$2$ are false
• D. Statement-$1$ are false , Statement-$2$ is true

Answer 1

The correct option is A Statement-$1$- is true, Statement-$2$- is true and Statement-$2$- is correct explanation for Statement-$1$.

Statement-1

As far as we concern about the properties of triangle the sum of two sides is always greater than the third side

It will form two triangle

In $\Delta$ ABP

AP+BP>AB

Also In $\Delta$ACP

AP+CP>AC

statement-2

It is correct since ,IT follows the triangle property and is the correct explanation of statement-1.