Question

in the adjoining figure a b and ac are equal chords of a circle line m is parallel to the tangent of point a and intersect is a chord at point D and. E respectively prove that ad is equal to a e​

Answer 1

In the adjoining figure a b and ac are equal chords of a circle line m is parallel to the tangent of point a and intersect is a chord at point D and. E respectively

Consider the figure while going through the following steps

∠ ABC = ∠ ACB ( radius AB = AC)

∠ PAD = ∠ ADE          (∵ m ║ PAQ)

∠ QAE = ∠ AED

∠ B = ∠ ADE = ∠ PAD     ( ∵ BC ║ m)

∠ C = ∠ AED = ∠ EAQ

∴ ∠ ADE = ∠ AED

Therefore, AD = AE