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The lines L1:y-x =0 and L2: 2x+y =0 inte...

The lines `L_1`:y-x =0 and `L_2`: 2x+y =0 intersect the line `L_3` : y+2 =0 at P and Q respectively. The bisector of the acute angle between `L_1` and `L_2` intersects `L_3` at R
Statement - 1 : The ratio PR : PQ equals `2sqrt2 : sqrt5`
Statement - 2 : In any triangle , bisector of an angle divides the triangle into two similar triangle

A

Statement 1 is true, statement 2 is false.

B

Statement 1 is true, statement 2 is true, statement 2 is the correct explanation of statement1.

C

Statement 1 is true, statement 2 is true, statement 2 is not the correct explanation of statement 1.

D

Statement 1 is false, statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
A
Draw lines on coordinate axes as shown here.

From the geometry of angle bisector,
`(PR)/(RQ) = (OP)/(OQ) = (2sqrt(2))/(sqrt(5))`
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