PQRS is a cyclic quadrilateral with PQ = 11 RS = 19. M and N are point

1.	PQRS is a cyclic quadrilateral with PQ = 11 RS = 19. M and N are points on PQ and RS respectively such that PM = 6, SN = 7, and MN = 27. The length of the line segment formed when MN is extended from both side until it reaches the circle is ?
Answer» ong>ANSWER: Given PQRS is a cyclic QUADRILATERAL. ::Opposite angles of a cyclic quadrilateral are supplementary → Z PSR + < PQR = 180° Z PQR = 180° - 110° → Z PQR = 70° (2)2 * Z PQR = m(arc PR){The measure of an inscribed angle is half the measure of the arc intercepted by it.} m(arc PR) = 140° m(arc PQR) = 360° -140° = 220° {Using Measure of a major arc = 360°- measure of its corresponding minor arc} (3)side PQ = side RQ ::m(arc PQ) = m(arc RQ){Corresponding arcs of congruent chords of a circle (or congruent circles) are congruent} = m(arc PQR) = m(arc PQ) + m(arc RQ) = m(arc PQR) = 2 x m(arc PQ) = m(arc PQ) = 110° (4)In A POR, PQR + < QRP + Z RPQ = 180°{Angle sum property} → Z PRQ + 2 RPQ = 180° - Z PQR → 22 PRQ = 180° - 70° {::side PQ = side RQ} = Z PRQ = 55° I KNOW IT'S MESSED UP BUT PLZ MANAGE PLZ MARK AS BRAINLEST!!

PQRS is a cyclic quadrilateral with PQ = 11 RS = 19. M and N are points on PQ and RS respectively such that PM = 6, SN = 7, and MN = 27. The length of the line segment formed when MN is extended from both side until it reaches the circle is ?

Answer»

Given PQRS is a cyclic QUADRILATERAL.

::Opposite angles of a cyclic quadrilateral are

supplementary

→ Z PSR + < PQR = 180°

Z PQR = 180° - 110°

→ Z PQR = 70°

(2)2 * Z PQR = m(arc PR){The measure of an

inscribed angle is half the measure of the arc

intercepted by it.}

m(arc PR) = 140°

m(arc PQR) = 360° -140° = 220° {Using

Measure of a major arc = 360°- measure of

its corresponding minor arc}

(3)side PQ = side RQ

::m(arc PQ) = m(arc RQ){Corresponding arcs

of congruent chords of a circle (or congruent

circles) are congruent}

= m(arc PQR) = m(arc PQ) + m(arc RQ)

= m(arc PQR) = 2 x m(arc PQ)

= m(arc PQ) = 110°

(4)In A POR,

PQR + < QRP + Z RPQ = 180°{Angle sum

property}

→ Z PRQ + 2 RPQ = 180° - Z PQR

→ 22 PRQ = 180° - 70° {::side PQ = side RQ}

= Z PRQ = 55°

I KNOW IT'S MESSED UP BUT PLZ MANAGE

PLZ MARK AS BRAINLEST!!