Question

Please guys answer the 17th one

Answer 1

Answer:

BD = BC (since <CBD = <BCD))

Step-by-step explanation:

From the figure we get <CAB = 30°

When we join O and C we get OC.

<COB = 2 * 30 = 60° because <A = 30° angle made by chord BC.

To find <CBD

Consider triangle BOC which is an isosceles triangletriangle, OB = OC = radius

Therefore, <OBC = <OCB = 60°

we get <CBD = 120° since <OBC = 60°( linear pair)

To find <BCD

We have CD is the tangent at C.

<OCD = 90 the <BCD = <OCD - OCB = 90 - 60 = 30°

To find <BDC

<BDC = 180 - (<CBD + <BCD) = 180 - ( 120 + 30) = 180 - 150 = 30°

From the above information we get,

BD = BC (since <CBD = <BCD)