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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.

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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.

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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.

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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.

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

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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.

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

Solution not provided.

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Short Answer Type

419.

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

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420.

In the given Fig, ∠ACB = 90°, CD ⊥ AB, prove that CD² = BD . AD.

118 Views