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TO Number and AD are bisectors of and PAC IZBAC = 30 prove A (3) C HD is a diameter of the circle. () (in ABC is an isosceles triangle. 345.000/-. The wholesaler il

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Q1

In the given figure PQ is a tangent to the circle at A. AB and AD are bisectors of

∠

CAQ and

∠

PAC. If

∠

BAQ

= 30^{o}

, prove that.
(I) BD is a diameter of the circle.
(II) ABC is an isosceles triangle.

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Q2

ABC is an isosceles triangle in which

A B = A C

.

A D

is the bisector of exterior angle

P A C

and

C D

is parallel to

A B

. Prove that
(i)

∠ D A C = ∠ B C A

(ii)

A B C D

is parallelogram.

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Q3

In figure ABC is an isosceles triangle in which AB = AC. CP || AB and AP is the bisector of exterior

∠ C A D o f △ A B C

. Prove that

∠ P A C = ∠ B C A

and ABCP is a parallelogram.

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Q4

ABC is an isosceles triangle in which AC = BC. AD and BE are angle bisectors of ∠CAB and ∠ABC. Prove that AE = BD.

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Q5

In fig. ABC is an isosceles triangle in which

A B = A C . C P | | A B a n d A P

is the bisector of exterior ∠CAD of ΔABC. Prove that

∠ P A C = ∠ B C A

and

A B C P

is a parallelogram.

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