Help with O level A Maths Geometric Proofs

Need help with question 19c), 19d and 22b :(

sound difficult , i let others answer you better :)

Need help with question 19c), 19d and 22b :(

Dear TS,

May I know where do the questions come from ie from your maths teacher, a book

etc ?

Thank you for your kind attention.

Regards

Lee012Lee

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Question 19

(a) Make use of the angle in a semi circle ie the midpoint of BP will be the

centre

(b) It is to be noted that t = s and make use of angles in the same segment.

ie NC will be s.

At A, draw a perpendicular line to the parallel line to meet at D.

Using similar triangles,

TM/TB = ND/NA

Since NC < ND < NA,

r/p > s/u

(d) Since NC < ND < NA,

s < u (shown)

Note : The questions should have asked to show that s < u first before it asks to

show s/u < r/p

Question 22

(a) Use the AAA Rule to prove the similar triangles

(b) Use the ASA rule to prove that triangle PTS is congruent to RTS.

Since the two triangles are congruent, SP = SR

An easier method is to extend the line SP and BQ to meet at D to form

triangles and use the ratio theorem to show that RO=0.5(BS+QP)