Q 14& 15
14. AB is a diameter and AC is a chord of a circle with centre 'O' such that The tangent at 'C' intersects extended AB at a point D. Prove that BC = BD.
15. A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.
From the Figure,
∠ACB = 
(Angle in semicircle)
⇒∠ABC = 
Also,
∠OCD =
and ∠ABC= ∠OBC =∠OCB = 
(
OB=OC)
⇒∠BCD= ∠OCD -∠OCB=
Since,
∠ABC=∠BCD+∠BDC
∠BDC=∠ABC-∠BCD=
Hence,
∠BCD=∠BDC
⇒BC= BD