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Triangles

Long Answer Type

411. D and E are points on the sides AB and AC respectively of ∆ABC such that DE is parallel to BC and AD : DB = 4:5. CD and BE intersect each other at F. Find the ratio of the areas of ∆DEF and ∆BCF.

510 Views

412. Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC prove that AP × PC = BP × PD.

618 Views

413. D is a point on the side BC of ∆ABC. Such that ∠ADC and ∠BAC are equal. Prove that CA² = DC × CB.

86 Views

Short Answer Type

414. In a right angled triangle ABC ∠A = 90° and AD ⊥ BC. Prove that AD² = BD × CD.

70 Views

415. In the given Fig, ABCD is a trapezium in which AB is parallel to DC. If AC trisect BD, then prove that CD = 1/2 AB.

145 Views

416. In ∆ABC, if AD is the median, show that AB² + AC² = 2 (AD² + BD²).

139 Views

Long Answer Type

417.

In the given Fig., ABC is a right triangle right angled at B. AD and CE are the two medians drawn from A and C respectively. If AC = 5 cm and $space space AD equals fraction numerator 3 square root of 3 over denominator 5 end fraction cm comma$ find the length of CE.

170 Views

418. Prove that the sum of the squares of the sides of a rhombus is equal sum of the squares on its diagonals.

131 Views

Short Answer Type

419.

In the given Fig. PA, QB and RC are each perpendicular to AC. Prove that $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$