Question

If pa and pb are tangent from p to a circle with center o if angle aob=130°then angle apb=?

Answer 1

Answer:

$\red {\angle APB}\green { = 50\degree }$

Step-by-step explanation:

$PA \: and \: PB \: are \: tangents \: from \: P\\to \: a \: circle \: whose \: center \:is \: O .$

$\angle AOB = 130\degree$

$\angle OBP = 90\degree\\and \: \angle OAP = 90\degree \: ( Tangent \: radius \: relation )$

$In \: AOBP \: quadrilateral ,\\\angle AOB + \angle OBP + \angle APB + \angle OAP = 360\degree$

$\implies 130 + 90 + \angle APB + 90 = 360\degree$

$\implies 310 + \angle APB = 360$

$\implies \angle APB = 360 - 310 = 50\degree$

Therefore.,

$\red {\angle APB}\green { = 50\degree }$

•••♪