In the given figure {\PQ} is a tangent to the circle at {\A} . {\AB} and {\AD} are bisectors of \angle {\CAQ} and \angle {\PAC}. IF \angle {\BAQ}=30^{\circ}, prove that: (i) {\BD} is a diameter of the circle. (ii) {\ABC} is an isosceles triangle.

ICSE Class X Math 2017 Solved Paper - Question 22

Question : 22 of 31

Marks: +1, -0

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^{∘}

, prove that:
(i)

{\BD}

is a diameter of the circle.
(ii)

{\ABC}

is an isosceles triangle.

Solution:

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