In the given figure, $∠ A B E = 40^{\circ}$ and EB bisects the angle between AB and tangent at B.CB bisects $∠ A B E .$ The measure of $∠ E C B$ is ___

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Solution

The correct answer is 60 $^{\circ}$ . Check the video for the approach.

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B

¯ ¯¯¯¯¯¯ ¯ A C, ¯ ¯¯¯¯¯¯¯ ¯ B D

∠ A B E

¯ ¯¯¯¯¯¯ ¯ B E

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∠ D B E

In the given figure, two circles touch each other externally at point $P$ . $A B$ is the direct common tangent of these circles. Prove that :

(i) tangent at point $P$ bisects $A B$ ,

(ii) angle $A P B =$ $90^{\circ}$ .

In a circle of radius 10 cm given below, chord AB and CD are equal. If OE bisects AB and OF bisects CD and OF = 6 cm, then length EB is ________ .

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