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BX and CY are the bisectors of angles ABC and ACB respectively. AB =AC and BY =4cm. What is the length of AX?

BX and CY are the bisectors of angles ABC and ACB respectively. AB =AC and BY =4cm. What is the length of AX? 

Question Image
Grade:10

2 Answers

Aditya Gupta
2075 Points
one year ago
join OA. note that OA will be perpendicular to BC since AB=AC. since ABC is isosceles and BX and CY are the angle bisectors , angles ABX= XBC= ACY= YCB= y (say)
now, join XO. and by inscribed/central angle theorem we have angle AOX= 2*ABX= 2y
similarly join YO and BO, so that angle BOY= 2*BCY= 2y
since chords BY and AX subtend equal angles (2y) at the centre of the circle, they both must be equal.
so, AX= BY= 4cm
kindly approve :))
Vikas TU
14149 Points
one year ago
Dear student
ABC is an isosceles triangle. Since AB = AC, angle B = angle C, so their half angles will be equal.
In triangles ABX and ACY,
Angle ABX (half of angle B) = and ACY (half of angle C)
AB = AC, and
A is common to both,
So the two triangles are congruent. Therefore BX = CY=AX 
Hope this will help 
Good Luck 
 

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