Welcome to Test-paper.info
Saturday, February 24 2018 @ 03:22 PM CST
 Select a Forum » General Chat » Primary 1 Matters » Primary 2 Matters » Primary 3 Matters » Primary 4 Matters » Primary 5 Matters » Primary 6 Matters » Question, Feedback and Comments » Education Classified
 Forum Index >  General Chat >  General Chat Need help on Sec 2 math questions
 | Printable Version
 By: Kuro (offline)  Monday, June 15 2015 @ 10:25 AM CDT (Read 1445 times)
Kuro

Kindly help solve the 2 questions. Thanks.

Junior

Registered: 12/31/06
Posts: 27

 By: echeewh (offline)  Sunday, June 28 2015 @ 01:46 PM CDT
echeewh

Hey <Kuro>

Following are my worked solutions:

Q1. (Refer to attached diagram)

Join the line OA. And triangles OBA, OCA are congruent {(RHS): angle OBA = 90 = angle OCA, OB = OC (radii), OA is common side}.

Angle AOB = angle AOC

Angle COB = 180 - 50 = 130
So angle AOB = 65 = angle AOC

Joining OD (radius), triangle ODB is isosceles {OD = OB (radii) }

Hence angle OBD = 65 ÷ 2 = 37.5 degrees {exterior angle of triangle ODB = sum of interior opposite angles}

=====

Q2. (Refer to attached diagram)

Triangles PQR, PST are equilateral and SR = SQ {given S is mid-point of QR}

PS is a line segment bisector and angle PSQ = 90 = angle PSR.

angle SPR = 90 - angle PRS = 90 - 60 = 30

Let the two lines PR and ST intersect at a point U.

Angle RSU = 90 - angle PST = 90 - 60 = 30

Angle RUS = angle USP + angle UPS = 60 + 30 = 90

Area RST = (1/2)(ST)(RU)
Area PQR = (1/2)(QR)(PS)

Since ST = PS,
(Area PST) / (Area PQR) = (RU) / (QR)

But QR = PR,
(Area PST) / (Area PQR) = (RU) / (PR)

Refer triangles RUS, PSR (both right-angled triangles).

In triangle RUS,
Sin (30) = (RU / RS) = (1/2)
RU = (1/2)(RS) = (RS)/2

In triangle PSR,
Sin (30) = (RS / PR) = (1/2)
PR = 2(RS)

Hence,
(Area PST) / (Area PQR) = (RU) / (PR)
= (RS)/2 ÷ 2(RS)
= 1/4

======

Trust this helps

Do let me know again if these are different from your <Anskey> or if there's further clarification.

Cheers,
Edward

Active Member

Registered: 04/21/11
Posts: 627

 All times are CST. The time is now 03:22 pm.
 Normal Topic Locked Topic Sticky Topic
 New Post Sticky Topic w/ New Post Locked Topic w/ New Post
 View Anonymous Posts Able to Post HTML Allowed Censored Content