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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?

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11 months 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= 2ysimilarly join YO and BO, so that angle BOY= 2*BCY= 2ysince chords BY and AX subtend equal angles (2y) at the centre of the circle, they both must be equal.so, AX= BY= 4cmkindly approve :))
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11 months ago
```							Dear studentABC 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, andA is common to both,So the two triangles are congruent. Therefore BX = CY=AX Hope this will help Good Luck
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11 months ago
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