in the given figure, P is anypoint on the chord BC of acircle such tha

1.	in the given figure, P is anypoint on the chord BC of acircle such that AB AP.Prove that CPCQ.3)
Answer» Given: P is a point on the chord BC. such that AB = AP To prove: CP = CQ Solution: in the triangle ABP, AB = AP therefore ∠ABP = ∠APB........(1) Angle subtended by the chord at the circumference are equal. ∠ABC = ∠AQC [angles subtended by the chord AC at circumference ] ∠ABP = ∠AQC ..........(2) [∠ABC = ∠ABP same angle] ∠APB = ∠CPQ ......(3) from (1), (2) and (3) ∠CPQ = ∠AQC i.e. ∠CPQ = ∠PQC Hence CP = CQ [sides opposite to equal angles are equal] Like if you find it useful

in the given figure, P is anypoint on the chord BC of acircle such that AB AP.Prove that CPCQ.3)

Answer»

Given: P is a point on the chord BC. such that AB = AP

To prove: CP = CQ

Solution:

in the triangle ABP, AB = AP

therefore ∠ABP = ∠APB........(1)

Angle subtended by the chord at the circumference are equal.

∠ABC = ∠AQC [angles subtended by the chord AC at circumference ]

∠ABP = ∠AQC ..........(2) [∠ABC = ∠ABP same angle]

∠APB = ∠CPQ ......(3)

from (1), (2) and (3)

∠CPQ = ∠AQC i.e. ∠CPQ = ∠PQC

Hence CP = CQ [sides opposite to equal angles are equal]

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