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Manish Kumar

· started a discussion

· 1 Months ago

check my solution (Question: 195170.0 )

CZY =CBY(on same arc)
CBY=30

OB =OC (circumradius)
BCZ=30
BCZ=BYZ(ON SAME ARC)

so BYZ=30

is solution me galti kha h????

Question:
In a \(\Delta\)ABC the internal bisector of the angles \(\angle \)A, \(\angle \)B and \(\angle \)C intersect the circumcircle at X, Y & Z. If \(\angle \)A = 50º, \(\angle \)CZY = 30º, then \(\angle \)BYZ will be
Options:
A) 35º
B) 30º
C) 45º
D) 55º
Solution:

Knowledge Expert

· commented

· 1 Months ago

Dear Student,

See step by Step:

Step i) Let I be the meeting point of all 3 internal bisectors, that is AX, BY & CZ.

Step ii) So <BIC = 90° + A/2 = 90° + 50°/2 = 115°
[In triangle BIC, <BIC = 180° - (1/2)(B + C) = 180° - (1/2)(180° - A) = 180° - 90° + A/2 = 90° + A/2]

Step iii) So <ZIY = <BIC = 115° [Vertically opposite angles equal]

Step iv) So from triangle ZIY,

<BYZ = 180° - (<ZIY + <CZY) = 180° - (115° + 30°) = 35°

Thus <BYZ = 35°

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