Ans pls its urgent: 22 AB is the diameter of a given circle with centre O - Maths - Sets

Question

Ans pls its urgent:

22 AB is the diameter of a given circle with centre O If PA=PB and
∠ PAC=20o, find the value of ∠ PAB and
∠ ABC

Neha Sethi · Accepted Answer

Dear student

Given: PA=PB⇒∠PAB=∠PBA=x sayAlso, ∠APB=90°  angle in a semicircleConsider △PAB, by angle sum property∠PAB+∠ABP+∠APB=180°⇒x+x+90°=180°⇒2x=90°⇒x=45°So, ∠PAB=45°Also, ∠ACB=90°  angle in a semicircleand ∠CAB=∠PAB-∠PAC=45°-20°=25°Consider △CAB, by angle sum property∠CAB+∠ABC+BCA=180°25°+∠ABP+∠PBC+90°=180°25°+45°+∠PBC+90°=180°∠PBC=20°So, ∠ABC=∠ABP+∠PBC=45°+20°=65°
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Ans pls its urgent: 22. AB is the diameter of a given circle with centre O. If PA=PB and ∠ PAC=20o, find the value of ∠ PAB and ∠ ABC.

Ans pls its urgent:

22. AB is the diameter of a given circle with centre O. If PA=PB and $∠$ PAC=20^o, find the value of $∠$ PAB and $∠$ ABC.