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Question

In the figure; PA is a tangent to the circle. PBC is secant and AD bisects angle BAC. Select the statements that are true.


A

CAD=13(PBAPAB)

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B

Triangle PAD is an isoscles triangle

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C

CAD=12(PBAPAB)

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D

CAD=19(PBAPAB)

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Solution

The correct options are
B

Triangle PAD is an isoscles triangle


C

CAD=12(PBAPAB)


Given - In a circle PA is the tangent. PBC is the secant and AD is the bisector of BAC which meets the secant at D.

PA is the tangent and AB is chord.

PAB=C

(Angles in the alt. segment)

AD is the bisector is BAC

1=2

In ΔADC,

Ext. ADP=C+1=PAB+2=PAD

ΔPAD is an isosceles triangle.

(ii) In ΔABC,

Ext. PBA=C+BAC

BAC=PBAC

1+2=PBAPAB [from (i)]

21=PBAPAB

1=12 [PBAPAB]

CAD=12 [PBAPAB]


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