Question

1. In A LMN, bisectors of ZL and 2M meet at P. If ZN= 90°. Find LLPM.
In the adioining figure​

Answer 1

ANSWER

Consider △LMN

MR perpendicular to LN and LM perpendicular to LN

∴ By property of geometric mean, MR

2

=LR.RN....(i)

Similarly in △LKN,

KR perpendicular to LN and LK perpendicular to KN

⇒KR

2

=LR.RN....(ii)

∴ From (i) and (ii)

MR

2

=KR

2

⇒MR=KR

∴R is the midpoint of segment MK

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