Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
Question 132
A cyclic quadrilateral ABCD is such that AB = BC, AD = DC, AC ⊥ BD, ∠CAD = θ. Then the angle ∠ABC =
Solution
AB = BC and AD = DC , $$\angle CAD = \theta$$
In isosceles $$\triangle$$ADC
=> $$\angle$$CAD + $$\angle$$ACD + $$\angle$$CDA = 180
=> $$2\theta$$ + $$\angle$$CDA = 180
=> $$\angle$$CDA = 180 - $$2\theta$$
Sum of opposite angles in a cyclic quadrilateral = 180
=> $$\angle$$CDA + $$\angle$$ABC = 180
=> $$\angle$$ABC + 180 - $$2\theta$$ = 180
=> $$\angle$$ABC = $$2\theta$$
Create a FREE account and get:
- Free SSC Study Material - 18000 Questions
- 230+ SSC previous papers with solutions PDF
- 100+ SSC Online Tests for Free
