Given: ABC is an isosceles triangle with AB = AC. A circle through B and C intersects AB and AC at D and E respectively.
To Prove: BC || DE
Proof: In ∆ABC,
∵ AB = AC
∴ ∠B = ∠C ...(1)
| Angles opposite to equal sides of a triangle are equal
∵ BCED is a cyclic quadrilateral
∴ ∠ADE = ∠C ...(2)
| An exterior angle of a cyclic quadrilateral is equal to its interior opposite angle
From (1) and (2),
∠ADE = ∠B
But these angles form a pair of equal corresponding angles
∴ DE || BC
5. In the given figure, find the values of a, b, c and d. Given that ∠BCD = 43° and ∠BAE = 62°.