Question

solve thia sum of circles

Answer 1

GIVEN :

ABCD is a cyclic quadrilateral

EC is the tangent to the circle

angle ABC=93°

angle DCE=35°

TO FIND :

angle ADC=?

angle CAD=?

angle ACD=?

SOLUTION :

as ABCD is a cyclic quadrilateral

by the property that opposite angles angles are supplementary

angle ABC + angle ADC=180

so 93 + angle ADC=180

angle ADC=180-93

angle ADC=87°

now,

as EC is a tangent and CD is a chord

by tangent chord theorem

angle DCE=angle CAD

so angle CAD=35°

now,

in triangle ACD

by angle sum property

angle CDA+angle ADC +angle ACD=180

so angle ACD+35+87=180

angle ACD=180-122

angle ACD=58°

so the measures of required angles are

angle ADC=87°

angle CAD=35°

angle ACD=58°