Question

In a circle with Centre P ab and CD are equal chords if angle APB is equal 100 degree then find angle P CD

Answer 1

Answer:

Chord AB =Chord CD

Angle APB=100 degree

Therefore angle CPD =100 degree

Answer 2

$\angle PCD=40^{\circ}$

Step-by-step explanation:

Center of the circle=p

Two chords AB  and CD

AB=CD

Angle APB=100 degrees

We know that

Equal chords subtended equal at center of circle.

Therefore, angle APB=Angle CPD=100 degrees

PC=PD=Radius of circle

Let angle PCD=angle PDC=x

Angle made by equal sides are equal.

In triangle PCD

$\angle PCD+\angle CDP+\angle CPD=180^{\circ}$

Using triangle angles sum property

Substitute the values then, we get

$x+x+100=180$

$2x=180-100=80$

$x=\frac{80}{2}=40$

$\angle PCD=40^{\circ}$

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