Question

In the given figure,O is the the centre of the circle. Determine angle APC, if DA and DC are tangents and angle ADC=50o.

Answer 1

Answer:

Step-by-step explanation:

Join OA and OC.

We know that tangent to a circle is always ⊥ to its radius at the point of contact

So, OA⊥DA and OC⊥DC.

In quad,  AOCD,∠ADC + ∠DAO + ∠DCO + ∠AOC = 360°  [Angle sum property]

⇒50° + 90° + 90° + ∠AOC = 360°⇒230° + ∠AOC = 360°⇒∠AOC = 130°

Now, reflex∠AOC = 360° − ∠AOC  = 360° − 130° = 230°

We know that angle subtended by an arc at the centre is double the angle subtended by the same arc atany point on the circle.So, reflex

∠AOC = 2∠APC⇒∠APC = 230°/2 = 115°