In the figure, APQ is a semicircle. QP is produced to B and BA is a tangent to the circle at A. Suppose AC┴PQ, PC:CQ=1:4 and AB=8cm.
(a) Consider triangle APC and triangle ACQ, show that AC^(2) =PC*QC.
(b) Show that AP*AB=AQ*BP.
(c) If PC=k, express AP and AQ in terms of k.
(d) Find the length of BP.
(e) Hence find the radius of the semicircle.

Question

In the figure, APQ is a semicircle. QP is produced to B and BA is a tangent to the circle at A. Suppose AC┴PQ, PC:CQ=1:4 and AB=8cm.
(a) Consider triangle APC and triangle ACQ, show that AC^(2) =PC*QC.
(b) Show that AP*AB=AQ*BP.
(c) If PC=k, express AP and AQ in terms of k.
(d) Find the length of BP.
(e) Hence find the radius of the semicircle.

anonymous · Answer

|dw:1359971354177:dw|

anonymous · Answer

|dw:1359978719506:dw|
$$AP^2+AQ^2=PQ^2$$
$$AC^2+CQ^2=AQ^2$$
subtract 1 from 2