Question

in any triangle xyz the bisector angle Y and angle Z meet at I from point O,op perpendicular Y Z ,oq perpendicular zx and or perpendicular xy respectively prove that PQ equal to oq equal to or

Answer 1

Refer to image for answer.

Answer 2

Step 1:

To Prove: OP=OQ=OR

Proof:  

In ΔYRO and  

∠RXO=∠PYO [because YO is the bisector of ∠Y]

∠YRO=∠YPO [each equal to 90°]

YO = YO [common]

Step 2:

⇒OP = OR (cpct) ... (i)

Step 3:

Similarly,  

In ΔZPO and ΔZQO,  

⇒OP = OQ (cpct).... (ii)

And In

Step 4:  

ΔXRO and ΔXQO,  

⇒OQ = OR (cpct)..... (iii)

From (i), (ii) and (iii), we get

Step 5:

OP = OQ = OR