Let: ∠BAD=a, BD = s.

∵□ABCD*** circle,

∴∠BCD= 180 -a

In △BAD and △BCD,

Have S2 = 2 2+3 2-2× 2× 3× COSA =12+4 2-2 * 4 * cos (180-a)? ,

∴cosa=- 1/5

∴? sina=√( 1-cosa^2)=√(24/25)？

∴s=√(2^2+3^2-2×2×3×cosa)=√(77/5)

∴ circumscribed circle radius r = √ (77/5)/(2sina) = (1/24) √ 2310?

2. This is the 2009 Peking University independent entrance examination.

Attachment: peking university independent recruitment Science Examination Questions in 2009-Mathematics?

1. The planar quadrilateral ABCD has a circumscribed circle, AB= 1, BC=2, CD=3, and DA=4. Find the radius of the circumscribed circle.

2. Infinitely positive arithmetic progression has 13, 25, 4 1, and the verification in 2009 is one of them.

3. Is there an X that makes tanx+ radical number 3 and cotx+ radical number 3 rational numbers?

4. If any X has acosx+bcos2x greater than or equal to-1, find the maximum value of A+B. ..

5. 333 students answered correctly 1000 questions. If they answered no more than three questions correctly, they failed; if they answered no less than six questions correctly, they were excellent. Which is more, failure or Excellence?