Thursday

December 18, 2014

December 18, 2014

Posted by **Bo** on Friday, May 25, 2012 at 3:17pm.

- math -
**MathMate**, Friday, May 25, 2012 at 5:42pmTake a piece of paper and note the following on your diagram. It will be difficult to follow without an annotated diagram.

Label the (horizontal) diameter as CD, with C on the left.

Label the chord 16 units long as PA (P on the left).

Label the chord 12 units long as QB (Q on the left).

Label the centre of the circle as O.

Construct a (vertical) diameter perpendicular to CD. Label the ends as E (on top) and F (at the bottom).

Label the intersection PA and EF as X, and the distance OX=x.

Label the intersection QB and EF as Y, and the distance OY=y.

Label the radius of the circle as r = OD.

Confirm that:

OD=OE=OC=OF=r=10

PX=XA=8

QY=YB=6

We don't know yet the distances x and y.

By the theorem of intersection of chords, we have

PX*XA = FX*XE

8²=(10-x)(10+x)

Solve for x to get 6.

θ1=∠AOD=sin^{-1}(6/10)

Similarly,

QY*YB=(10-y)(10+y)

6²=(10-y)(10+y)

Solve for y to get 8.

θ2=∠BOD=sin^{-1}(6/10)

⇒

φ=∠BOA=θ2-θ1

Arc length of AB

=rφ/2π

=10φ/2π

**Answer this Question**

**Related Questions**

Geometry - in circle p below the lengths of the parallel chords are 20,16, and ...

geometry - given: chord AB is parallel to chord CD prove if two chords of a ...

gometry - in a circle of radius 17cm, two parallel chords are drawn on opposite ...

Math - Two chords intersect inside a circle. The lengths of the segment of one ...

Geometry - The question is to find the measure of arc PQ in Circle A. The point ...

geometry - Two chords intersect a circle. The shorter chord is divided into ...

circle - two parallel chords of length 30 cm and 16 cm are draw on the opposite ...

circle - two parallel chords of length 30 cm and 16 cm are draw on the opposite ...

Math - In a circle , the radius is 68 units and a chord of the circle is 120 ...

Math - In a circle , the radius is 68 units and a chord of the circle is 120 ...