Solution: (1) Proof: Connect OE, BE,

∵AB is the diameter.

∴BE⊥AC.

∵D is the midpoint of BC,

∴DC=DB.

∴∠DBE=∠DEB.

And OE=OB,

∴∠OBE=∠OEB．

∴∠DBE+∠OBE=∠DEB+∠OEB.

That is, ∠ABD=∠OED.

But ∠ABC=90°,

∴∠OED=90°.

∴DE is the tangent of ⊙O.

(2) Method 1: ∵∠ABC=90°, AB=23, BC=2DE=6,

∴AC=43.

∴BE=3.

∴AE=3;

Method 2: ∵AC＝AB2+BC2＝(23)2+62＝43 (8 points)

∴BE =AB?BCAC=2 Liked and Disliked What is your evaluation of this answer? Comments are closed // High quality or satisfactory or special type or recommended answer. Time window.iPerformance && window.iPerformance.mark('c_best', +new Date); Recommended lawyer service: If your problem is not solved, please provide details Describe your problem and get free professional consultation through Baidu Lulin. Other similar problems 2012-01-03 As shown in the figure, △ABC is a right triangle, ∠ABC=90°, and ⊙O with AB as the diameter intersects AC at point E , point D is the midpoint of side BC, connecting DE. 1552012-12-16 As shown in the figure, △ABC is a right triangle, ∠ABC=90°, ⊙O with AB as the diameter intersects AC at point E, point D is the midpoint of side BC, and connects DE. 212010-10-18 As shown in the figure, in triangle ABC, angle B = 2 angle C, AD is perpendicular to BC and D, and M is the midpoint of BC. Verify: DM=1/2AB492014-02-12As shown in the figure, in triangle ABC, angle ACB=90°, angle B>angle A, point D is the midpoint of side AB, DE is parallel to BC and intersects AC at point E2512012-06 -23 Known: As shown in the figure, in the right triangle ABC, ∠BAC=90°, AB=AC, D is the midpoint of BC 122011-10-26 In the Rt triangle ABC, the angle ABC=90 degrees.

Circle O with AB as diameter intersects AC at point D, E is the midpoint of CB, and straight line ED intersects with the extension line of AB at F.42020-02-09 (2011? Tai'an) Known: In △ABC, AC= BC, ∠ACB=90°, point D is the midpoint of AB, and point E is a point on the side of AB. 42013-12-12 △ABC is a right triangle, angle ABC = 90 degrees, ⊙O with AB as diameter intersects AC at point E, point D is the midpoint of side BD. Verify: 2 More similar questions?> For you Recommended: F.context('cmsRight', [ { 'url':'/d01373f082025aaf511aa256e9edab64034f1a07?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_450%2Ch_600%2Climit_1%2Fquality%2Cq_85%2Fformat%2C f_auto', ' contractId':'A24KA00562', } ]); The price of electric vehicles has been reduced many times, is the quality guaranteed? What impact will the “cyber toilet” have? Are second-hand mobile phones in Huaqiangbei reliable? Why are cancer treatment costs increasing? Recommended for you F.context('recBrand',[{"img":"\/86d6277f9e2f07083523f69dfb24b899a901f20d?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_450%2Ch_600%2Climit_1%2Fquality%2Cq_85% 2Fformat%2Cf_auto"," url":"/hm.js?6859ce5aaf00fb00387e6434e4fcc925"; var s = document.getElementsByTagName("script")[0]; s.parentNode.insertBefore(hm, s); })(); window.tt = 1722613943;< /p>