Question

Two circles intersect at two points B and C.Through B two line segment ABD and PBQ are drawn to intersect the circle at A,D and P,Q respectively.Prove that angle ACP=angleQCD​

Answer 1

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⇒Chords AP and DQ are joined.

⇒For chord AP,

⇒∠PBA=∠ACP        ...Angles in the same segment --- (i)

⇒For chord DQ,

⇒∠DBQ=∠QCD        ...Angles in same segment --- (ii)

⇒ABD and PBQ are line segments intersecting at B.

⇒∠PBA=∠DBQ        ...Vertically opposite angles --- (iii)

By the equations (i), (ii) and (iii),

∠ACP=∠QCD

Answer 2

Answer:

Solution since angle in the same segment of a circle are equal

Step-by-step explanation:

.: /_ABP>=/_ACP ....... But,/_ABP=/_DBQ

equ i and,/_DBQ=/_DCQ(Angle in the same segment)

....equ ii from i and ii,we have

/_ACP=/_DCQ =>/_ACP=/_QCD