Question

8x + 277 +36X'y + 54xy*
In a A ABC.
i)
The
The sides AB and AC are produced to P
and Q respectively. If the bisectors of
ZPBC and ZQCB intersect at Apoint O.
Prove that ZBOC = 90°- ZA
The bisectors of ZB and
Prove that ZBOC = 90° +
C intersect each other at a point o.
ZA
2

Answer 1

Step-by-step explanation:

Angle BOC = 180 - (Angle CBO + Angle BCO) ----(1)

Since exterior angle of a triangle equal the sum of opposite interior angles, we have:-

Angle CBO = (1/2) angle CBP(Ext. angle) = (1/2) (Angle A + Angle C)

Angle BCO = (1/2) angle BCQ (Ext. angle) = (1/2) (angle A + angle B)

==> angle CBO + angle BCO

= (1/2)[(angle A+angleC) + (angle A + angle B)]

= (1/2)[ (angle A + angle B + angle C) + angle A]

= (1/2) ( 180 + angle A) = 90 + (1/2) angle A ------(2)

From (1) and (2),

Angle BOC = 180 - [90 + (1/2) angle A] = 90 - (1/2) angle A