In Fig. if AP = PB, thenA. AC = AB B. AC = BC C. AQ = QC D. AB = B

1.	In Fig. if AP = PB, thenA. AC = AB B. AC = BC C. AQ = QC D. AB = BC
Answer» Answer is B. AC = BC 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

In Fig. if AP = PB, thenA. AC = AB B. AC = BC C. AQ = QC D. AB = BC

Answer»

Answer is B. AC = BC

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

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In Fig. if AP = PB, thenA. AC = AB B. AC = BC C. AQ = QC D. AB = BC

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