Question

AB is a diameter of a circle O Chord CD is equal to radius OC. If AC and BD when produced intersect at P, prove that APB is 60°

Answer 1

Answer:

Step-by-step explanation:

Angle a is 90 and b is90 because tangent at any point of circle is perpendicular to the radius. So in triangle abvp = 90+90+anglep +90+90= 360angle p=60

Answer 2

Step-by-step explanation:

d is also a radius (given)

thus,Δocd is an equilateral triangle

so all angles are 60°

now..

oa║cd

so , ∠oca=60°

similiarly,

ob║cd

so, ∠odb=60°  ∠dcp=180-(60+60)° (linear pair)

⇒60°

similiarly,

∠cdp=180-(60+60)° (linear pair)  by angle sum property..

∠cpd=180-(60+60)°

⇒180-120°

⇒60°  hence proved

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