Question

In the adjoining figure, ABCD is a cyclic
quadrilateral. The line PQ is the tangent to the
circle at A. If ZCAQ : CAP = 1:2, AB bisects
ZCAQ and AD bisects ZCAP, then find the
measures of the angles of the cyclic quadrilateral.
Also prove that BD is a diameter of the circle.
B
P
A​

Answer 1

Answer:

yaar in which class are you well I seriously don't know if I know than I will definitely tell you na

bye

Answer 2

AB and AD are the bisectors of ZCAQ and ZCAP respectively and angle CAQ+angleCAB = 180° (linear pair)

.. angle CAB =angle CAD = 90°

angle BAD = 90°

Hence, BD is at diameter of the circle.

(ii). angleCAQ: angleCAP = 1:2

Let angleCAQx and angleCAP = 2x

x+2x= 180°( linear pair)