Question

In the given figure, ABCD is a cyclic
quadrilateral whose diagonals intersect at P
such that angle DBC = 60° and ZBAC = 40°.
Find (i) angle BCD, (ii) angle CAD.
​

Answer 1

Step-by-step explanation:

........................

Answer 2

Consider ∠CAD and ∠CBD

They are both angles made by the same chord CD

⟹∠CAD=∠CBD=30

∘

Since ABCD is a cyclic quadrilateral opposite angles are supplementary.

⟹∠DAB+∠DCB=180

∘

∠DCB=180

∘

–(∠DAC+∠CAB)

∠DCB=180

o

–30

o

–50

o

=100

∘Related Questions to study

In the figure at left, PQ is a diameter of a circle with centre O. If ∠PQR=55

o

,∠SPR=25

o

and ∠PQM=50

o

.

Find (i) ∠QPR,

(ii)∠QPM and

(iii) ∠PRS.

A rectangle ABCD in a intersected in in a circle with the centre O. if a AC is a diagonal and /_BAC then a radius of a circle is equal to