Question

In the given figure, if AB =PB, Then
(a) AC =AB
(B) AC=BC
(C) AQ=QC
(D) AB=BC​

Answer 1

Given:

AP = PB

Property: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal.

By the above property,

AP = AQ (tangent from A)

BR = BP (tangent from B)

CQ = CR (tangent from C)

Clearly,

AP = BP = BR

AQ = AP = BR

Now,

AQ + QC = BR + RC

⇒ AC = BC [∵AC = AQ + QC and BC = BR + RC]

Hence, AC = BC

Answer 2

Answer:

Option B

Step-by-step explanation:

AP=AQ (tangent from A)

BR=BP (tangent from B)

CQ=CR ( tangent from C)

AP=BP=BR

AQ=AP=BR

Now, AQ+QC=BR+AC

AC=BC (AC=AQ+QC & BC=BR+RC)

Hence AC=BC