Math, asked by nitumonineog42, 9 months ago

Two circles intersect each other at the point A and B. A point P an the circumference of one circle is joined with A and B and extended to meet the other circle at points C and D respectively. Prove that CD is parallel to the tangent at P to the circle on which P lies

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$<!DOCTYPE html><html lang="en"><head><title>Bts army bomb</title></head><body><div id="container" class="army-bomb-container"><div id="handle" class="handle"><div id="army-bomb" class="army-bomb"/></div><style>body {background: linear-gradient(45deg, #FBCCB7, #EFAAC9, #CCB6D9, #A2C8ED);width: 100vh;height: 300px;}.army-bomb-container {position: fixed;left: 50%;top: 50%;transform: translateX(-50%) translateY(-30%);}.handle {position: relative;height: 200px;width: 50px;background-color: black;z-index: 0;}/* top of the army bomb drawn using pseudo elements on the handle (so that it is drawn behind the glowing animation) */.handle:before {position: absolute;left: 132.5%;top: -30%;width: 30px;height: 10px;background-color: black;transform: rotate(45deg);z-index: -1;content: "";}.handle:after {position: absolute;left: 168.5%;top: -31.5%;width: 3px;height: 5px;background-color: red;transform: rotate(45deg);z-index: -1;content: "";}.army-bomb {position: relative;left: 50%;transform: translateX(-50%) translateY(-50%);width: 150px;height: 150px;background-color: white;border-radius: 75px;animation: light-up 3s infinite ease-in-out;}/* BTS logo drawn using pseudo elements of the army bomb */.army-bomb::before {position: absolute;top: 160%;left: 34%;border-bottom: 10px solid white;border-left: 10px solid transparent;border-right: 10px solid transparent;height: 0;width: 15px;transform: rotate(90deg);content: "";}.army-bomb::after {position: absolute;top: 160%;right: 34%;border-bottom: 10px solid white;border-left: 10px solid transparent;border-right: 10px solid transparent;height: 0;width: 15px;transform: rotate(-90deg);content: "";}/* glowing animation */@keyframes light-up {0% { box-shadow: 0px 0px 50px 1px white; }50% { box-shadow: 0px 0px 50px 30px white; }100% { box-shadow: 0px 0px 50px 1px white; }}</style></body></html>$

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Two circles intersect each other at the point A and B. A point P an the circumference of one circle is joined with A and B and extended to meet the other circle at points C and D respectively. Prove that CD is parallel to the tangent at P to the circle on which P lies​

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Two circles intersect each other at the point A and B. A point P an the circumference of one circle is joined with A and B and extended to meet the other circle at points C and D respectively. Prove that CD is parallel to the tangent at P to the circle on which P lies