Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    Hey, really stuck on this q, any help or clues to get started would be appreciated.

    "In the diagram AB=6cm is the diamater of the circle and BT is the tangent to the circle at B. The chord AC is extened to meet this tangent at D and <DAB= theta
    a) Show that CD = 6(sec theta - cos theta)"

    If anyone has the edexcel C3 book the diagram is on p/82 and q.8
    Thnaks
    Offline

    2
    ReputationRep:
    (Original post by jimber)
    Hey, really stuck on this q, any help or clues to get started would be appreciated.

    "In the diagram AB=6cm is the diamater of the circle and BT is the tangent to the circle at B. The chord AC is extened to meet this tangent at D and <DAB= theta
    a) Show that CD = 6(sec theta - cos theta)"

    If anyone has the edexcel C3 book the diagram is on p/82 and q.8
    Thnaks
    ok the first thing to do is connect C to B so that you have a triangle ACB where angle acb =90 since angle in a semicircle is 90.And triangle ABD is also 90 , diameter is perpendicular to tangent. Now using trig find AD for triangle ABC , which is 6sectheta , similary find AC in triangle ABD which is 6costheta.
    so CD= 6(sectheta -costheta)
    Offline

    0
    ReputationRep:
    I got CD = 6* SinTheta*TanTheta by working out BD first

    Presumably that is the same thing.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by rbnphlp)
    ok the first thing to do is connect C to B so that you have a triangle ACB where angle acb =90 since angle in a semicircle is 90.And triangle ABD is also 90 , diameter is perpendicular to tangent. Now using trig find AD for triangle ABC , which is 6sectheta , similary find AC in triangle ABD which is 6costheta.
    so CD= 6(sectheta -costheta)
    Hey, thanks for the reply. Big help! I'll rep you in a mo
    Offline

    2
    ReputationRep:
    (Original post by jimber)
    Hey, thanks for the reply. Big help! I'll rep you in a mo
    thnx for the rep
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by stevencarrwork)
    I got CD = 6* SinTheta*TanTheta by working out BD first

    Presumably that is the same thing.
    Hey thanks, how did you work out BD? Just realised I have to use this method to answer the next part to the question lol
    Offline

    0
    ReputationRep:
    (Original post by jimber)
    Hey thanks, how did you work out BD? Just realised I have to use this method to answer the next part to the question lol
    DB and AB are at right angles. So BD/AB = tan Theta
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by stevencarrwork)
    DB and AB are at right angles. So BD/AB = tan Theta
    Thanks, the next part of the question told me CD was 16cm and asked if i cud calculate AC, but i thought i would need the length of AD to do this?
    Offline

    0
    ReputationRep:
    You have a formula for CD, so presumably you solve it for theta.

    What sort of triangle is ACB?
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by stevencarrwork)
    You have a formula for CD, so presumably you solve it for theta.

    What sort of triangle is ACB?
    I've got 6(sec theta - cos theta) = 16 but i'm not sure how to solve this, tried by multiplying by cos and replacing the cos's with x's and solving as a quadratic but it failed lol.

    umm ACB is just a normal triangle, no right-angles but i get the feeling angle >CAB = >ABT?
    Offline

    0
    ReputationRep:
    If AB is a diameter, what angle is at C?
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by stevencarrwork)
    If AB is a diameter, what angle is at C?
    DOH! i'm officialy retarded lol sorry about the late reply, but don't i still need to know one more thing before i can work out AC?
    Offline

    0
    ReputationRep:
    (Original post by jimber)
    I've got 6(sec theta - cos theta) = 16 but i'm not sure how to solve this, tried by multiplying by cos and replacing the cos's with x's and solving as a quadratic but it failed lol.
    It can't fail. The quadratic can be solved if you do what you did.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by stevencarrwork)
    It can't fail. The quadratic can be solved if you do what you did.
    raaa i must've made a mistake, for my quadratic i got:
    x^2 - (16x/6) - 1 = 0
    I tried to use the quadratic equation but it gave me answers >1
    Offline

    0
    ReputationRep:
    You must have a minus sign wrong.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by stevencarrwork)
    You must have a minus sign wrong.
    Yeah I did, thanks for your help, i'll rep you in a mo
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Would you like to hibernate through the winter months?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.