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♥️Bhavika Naik?? 7 years, 9 months ago
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Sia ? 6 years, 5 months ago

Let AB be a chord of a circle with centre O, and let AP and BP be the tangents at A and B respectively. Let the two tangents AP and BP meets at P.
Now Join OP. Suppose OP meets AB at C and the chord AB=AC+BC.
We have to prove that {tex}\angle P A C = \angle P B C{/tex}
In two triangles PCA and PCB, we have
PA = PB [{tex} \because{/tex}Tangents from an external point are equal]
{tex}\angle A P C = \angle B P C{/tex} [{tex} \because {/tex} PA and PB are equally inclined to OP]
and, PC = PC [Common]
So, by SAS-criterion of congruence, we obtain
{tex}\Delta P A C \cong \Delta P B C{/tex}
{tex}\Rightarrow \quad \angle P A C = \angle P B C{/tex}
Posted by Teerth Raj Chaudhary 7 years, 9 months ago
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Khushbu . 7 years, 9 months ago
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Nyayir Riba 7 years, 9 months ago
Nyayir Riba 7 years, 9 months ago
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Sia ? 6 years, 5 months ago
cos2 67° - sin2 23°
= cos2 67° - sin2 (90°- 67°)
= cos2 67° - cos2 67° [since, sin(90o-a) = cos a]
= 0
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Sia ? 6 years, 5 months ago

DE = EB = 1:3
In {tex}\triangle{/tex}AEB and {tex}\triangle{/tex}CED, {tex}\angle 1 = \angle 2{/tex} (alternate angles)
{tex}\angle 3 = \angle 4{/tex} (Vertically opposite angles.)
{tex}\therefore \quad \Delta \mathrm { AEB } \sim \Delta \mathrm { CED }{/tex}
{tex}\Rightarrow \quad \frac { \mathrm { AB } } { \mathrm { CD } } = \frac { \mathrm { BE } } { \mathrm { DE } } \Rightarrow \frac { \mathrm { AB } } { \mathrm { CD } } = \frac { 3 } { 1 }{/tex} [{tex}\because {/tex} DE: BE = 1:3]
{tex}\Rightarrow{/tex} AB = 3CD
Posted by Madhav Khurana 6 years, 5 months ago
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Sia ? 6 years, 5 months ago
Let the number be (3q + r)
{tex}n = 3 q + r \quad 0 \leq r < 3{/tex}
{tex}\text { or } 3 q , 3 q + 1,3 q + 2{/tex}
{tex}\text { If } n = 3 q \text { then, numbers are } 3 q , ( 3 q + 1 ) , ( 3 q + 2 ){/tex}
{tex}3 q \text { is divisible by } 3{/tex}.
{tex}\text { If } n = 3 q + 1 \text { then, numbers are } ( 3 q + 1 ) , ( 3 q + 3 ) , ( 3 q + 4 ){/tex}
{tex}( 3 q + 3 ) \text { is divisible by } 3{/tex}.
{tex}\text { If } n = 3 q + 2 \text { then, numbers are } ( 3 q + 2 ) , ( 3 q + 4 ) , ( 3 q + 6 ){/tex}
{tex}( 3 q + 6 ) \text { is divisible by } 3{/tex}.
{tex}\therefore \text { out of } n , ( n + 2 ) \text { and } ( n + 4 ) \text { only one is divisible by } 3{/tex}.
Posted by Mohit Rajput 7 years, 9 months ago
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Posted by Mohit Rajput 7 years, 9 months ago
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Yukku Malik 7 years, 9 months ago
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