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SHANTANU KUMAR SINGH

· started a discussion

· 1 Months ago

A POINT (Question:108026.0)

HOW OP=PC AND ANGLE COP =45..

Question:
In the given figure, the radius of the circle is 1 mtr. If AC = BD and CD is a tangent at point P, then the value of AC + CP will be:


Options:
A) 105 cm
B) 141.4 cm
C) 138.6 cm
D) 282.8 cm
Solution:
Ans: (b)

Given :

OA = OB = radius = 1 metre

\(\because\)AC = BD (Given)

\(\therefore \) OC = OD

Thus, the triangle COD is a right angled isosceles triangle.

\(\therefore\)\(\angle \)OCD = \(\angle \)ODC = 45°

In \(\triangle\)OCP,

\(\angle \)COP = 45° \(\Rightarrow\) OP = CP = 1

\(\therefore\) OC = OA + AC

\(\sqrt{2}=1+AC\Rightarrow AC=\sqrt{2}-1\)

A.T.Q.,

AC + CP = \(\sqrt{2}-1+1=\sqrt{2}= 141.4\) cm

manish malav

· commented

· 1 Months ago

Yet to be approved!
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