In the given figure AB is a diameter and CD is a tangent If AngleBDC = a and AngleBCD - Maths - Circles

Question

In the given figure AB is a diameter and CD is a tangent If
AngleBDC = a and AngleBCD = b, prove that 2a + b = 90

Anuradha Sharma · Accepted Answer

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In triangle BCD , ∠ABD is external angle so, ∠ABD=∠BCD+∠BDC=a+band CD is the tangent and ∠BAD is the angle in the alternate exterior so∠BAD=∠BDC=aNow in triangle ABD with AB as diameter 
∠ADB=90 angle in semicircleand using angle sum property, ∠ABD+∠ADB+∠BAD=180a+a+b+90=1802a+b=90Hence proved

In the given figure AB is a diameter and CD is a tangent. If AngleBDC = a and AngleBCD = b, prove that 2a + b = 90.